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Forecasting

Construction Engineering · FE Reference Handbook section

Construction Engineering
3 formulas
10 exam-style examples
~51 min
All Construction Engineering lectures

Core formulas for this FE topic

Definitions, applicability, units, assumptions and worked examples for each relation.

Worked exam-style examples

The four ways this section is written on the real exam — thoughts first, then equations, then substitution.

Example 1
Total cost from unit cost — solve for total cost — Forecasting

A construction engineering problem uses Total cost from unit cost. Given unit cost (cu) = 243.5 $/unit; quantity (Q) = 7,204 units, determine the total cost (C) in $.

Given

  • unit cost (cu) = 243.5 $/unit

  • quantity(Q)=7,204unitsquantity (Q) = 7,204 units

Find

total cost (C), in $

Start with the thinking

  • The governing relation printed in this handbook section is Total cost from unit cost.
  • Everything except C is given, so isolate C symbolically first — never rearrange after the numbers are in.
  • Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
  • Construction Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

  1. Step 1 — State the governing relation:

    C=cu×QC = c_u \times Q

  2. Step 2 — Rearrange the relation so that C stands alone on the left-hand side.

  3. Step 3 — List the givens: unit cost (cu) = 243.5 $/unit, quantity (Q) = 7,204 units.

  4. Step 4 — Substitute the given values into the rearranged relation.

  5. Step 5 — Evaluate:

    C=1754174 $C = 1754174\ \text{\$}

  6. Step 6 — Check: returning C = 1,754,174 $ to

    C=cu×QC = c_u \times Q

    reproduces the given quantities, and both sides carry the same units.

Answer:
C=1754174 $C = 1754174\ \text{\$}

Why the other options are there

  • 3,508,348 — kept a factor of two that cancels in the correct rearrangement.
  • 877,087 — dropped that same factor in the other direction.
  • 1,929,591 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Forecasting

Example 2
Total cost from unit cost — solve for unit cost — Forecasting (2)

A construction engineering problem uses Total cost from unit cost. Given quantity (Q) = 6,681 units; total cost (C) = 229,395 $, determine the unit cost (cu) in $/unit.

Given

  • quantity(Q)=6,681unitsquantity (Q) = 6,681 units

  • total cost (C) = 229,395 $

Find

unit cost (cu), in $/unit

Start with the thinking

  • The governing relation printed in this handbook section is Total cost from unit cost.
  • Everything except cu is given, so isolate cu symbolically first — never rearrange after the numbers are in.
  • Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
  • Construction Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

  1. Step 1 — State the governing relation:

    C=cu×QC = c_u \times Q

  2. Step 2 — Rearrange the relation so that cu stands alone on the left-hand side.

  3. Step 3 — List the givens: quantity (Q) = 6,681 units, total cost (C) = 229,395 $.

  4. Step 4 — Substitute the given values into the rearranged relation.

  5. Step 5 — Evaluate:

    cu=34.3354 $/unitcu = 34.3354\ \text{\$/unit}

  6. Step 6 — Check: returning cu = 34.3354 $/unit to

    C=cu×QC = c_u \times Q

    reproduces the given quantities, and both sides carry the same units.

Answer:
cu=34.3354 $/unitcu = 34.3354\ \text{\$/unit}

Why the other options are there

  • 68.6709 — kept a factor of two that cancels in the correct rearrangement.
  • 17.1677 — dropped that same factor in the other direction.
  • 37.7690 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Forecasting

Example 3
Total cost from unit cost — solve for quantity — Forecasting (3)

A construction engineering problem uses Total cost from unit cost. Given unit cost (cu) = 236.5 $/unit; total cost (C) = 335,181 $, determine the quantity (Q) in units.

Given

  • unit cost (cu) = 236.5 $/unit

  • total cost (C) = 335,181 $

Find

quantity (Q), in units

Start with the thinking

  • The governing relation printed in this handbook section is Total cost from unit cost.
  • Everything except Q is given, so isolate Q symbolically first — never rearrange after the numbers are in.
  • Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
  • Construction Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

  1. Step 1 — State the governing relation:

    C=cu×QC = c_u \times Q

  2. Step 2 — Rearrange the relation so that Q stands alone on the left-hand side.

  3. Step 3 — List the givens: unit cost (cu) = 236.5 $/unit, total cost (C) = 335,181 $.

  4. Step 4 — Substitute the given values into the rearranged relation.

  5. Step 5 — Evaluate:

    Q=1417 unitsQ = 1417\ \text{units}

  6. Step 6 — Check: returning Q = 1,417 units to

    C=cu×QC = c_u \times Q

    reproduces the given quantities, and both sides carry the same units.

Answer:
Q=1417 unitsQ = 1417\ \text{units}

Why the other options are there

  • 2,835 — kept a factor of two that cancels in the correct rearrangement.
  • 708.6 — dropped that same factor in the other direction.
  • 1,559 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Forecasting

Example 4
Total cost from unit cost — solve for total cost (case 2) — Forecasting (4)

A construction engineering problem uses Total cost from unit cost. Given unit cost (cu) = 146.5 $/unit; quantity (Q) = 3,225 units, determine the total cost (C) in $.

Given

  • unit cost (cu) = 146.5 $/unit

  • quantity(Q)=3,225unitsquantity (Q) = 3,225 units

Find

total cost (C), in $

Start with the thinking

  • The governing relation printed in this handbook section is Total cost from unit cost.
  • Everything except C is given, so isolate C symbolically first — never rearrange after the numbers are in.
  • Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
  • Construction Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

  1. Step 1 — State the governing relation:

    C=cu×QC = c_u \times Q

  2. Step 2 — Rearrange the relation so that C stands alone on the left-hand side.

  3. Step 3 — List the givens: unit cost (cu) = 146.5 $/unit, quantity (Q) = 3,225 units.

  4. Step 4 — Substitute the given values into the rearranged relation.

  5. Step 5 — Evaluate:

    C=472463 $C = 472463\ \text{\$}

  6. Step 6 — Check: returning C = 472,463 $ to

    C=cu×QC = c_u \times Q

    reproduces the given quantities, and both sides carry the same units.

Answer:
C=472463 $C = 472463\ \text{\$}

Why the other options are there

  • 944,925 — kept a factor of two that cancels in the correct rearrangement.
  • 236,231 — dropped that same factor in the other direction.
  • 519,709 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Forecasting

Example 5
Total cost from unit cost — solve for unit cost (case 2) — Forecasting (5)

A construction engineering problem uses Total cost from unit cost. Given quantity (Q) = 2,953 units; total cost (C) = 76,133 $, determine the unit cost (cu) in $/unit.

Given

  • quantity(Q)=2,953unitsquantity (Q) = 2,953 units

  • total cost (C) = 76,133 $

Find

unit cost (cu), in $/unit

Start with the thinking

  • The governing relation printed in this handbook section is Total cost from unit cost.
  • Everything except cu is given, so isolate cu symbolically first — never rearrange after the numbers are in.
  • Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
  • Construction Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

  1. Step 1 — State the governing relation:

    C=cu×QC = c_u \times Q

  2. Step 2 — Rearrange the relation so that cu stands alone on the left-hand side.

  3. Step 3 — List the givens: quantity (Q) = 2,953 units, total cost (C) = 76,133 $.

  4. Step 4 — Substitute the given values into the rearranged relation.

  5. Step 5 — Evaluate:

    cu=25.7816 $/unitcu = 25.7816\ \text{\$/unit}

  6. Step 6 — Check: returning cu = 25.7816 $/unit to

    C=cu×QC = c_u \times Q

    reproduces the given quantities, and both sides carry the same units.

Answer:
cu=25.7816 $/unitcu = 25.7816\ \text{\$/unit}

Why the other options are there

  • 51.5632 — kept a factor of two that cancels in the correct rearrangement.
  • 12.8908 — dropped that same factor in the other direction.
  • 28.3597 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Forecasting

Example 6
Total cost from unit cost — solve for quantity (case 2) — Forecasting (6)

A construction engineering problem uses Total cost from unit cost. Given unit cost (cu) = 249.5 $/unit; total cost (C) = 21,553 $, determine the quantity (Q) in units.

Given

  • unit cost (cu) = 249.5 $/unit

  • total cost (C) = 21,553 $

Find

quantity (Q), in units

Start with the thinking

  • The governing relation printed in this handbook section is Total cost from unit cost.
  • Everything except Q is given, so isolate Q symbolically first — never rearrange after the numbers are in.
  • Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
  • Construction Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

  1. Step 1 — State the governing relation:

    C=cu×QC = c_u \times Q

  2. Step 2 — Rearrange the relation so that Q stands alone on the left-hand side.

  3. Step 3 — List the givens: unit cost (cu) = 249.5 $/unit, total cost (C) = 21,553 $.

  4. Step 4 — Substitute the given values into the rearranged relation.

  5. Step 5 — Evaluate:

    Q=86.3848 unitsQ = 86.3848\ \text{units}

  6. Step 6 — Check: returning Q = 86.3848 units to

    C=cu×QC = c_u \times Q

    reproduces the given quantities, and both sides carry the same units.

Answer:
Q=86.3848 unitsQ = 86.3848\ \text{units}

Why the other options are there

  • 172.8 — kept a factor of two that cancels in the correct rearrangement.
  • 43.1924 — dropped that same factor in the other direction.
  • 95.0232 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Forecasting

Example 7
Total cost from unit cost — solve for total cost (case 3) — Forecasting (7)

A construction engineering problem uses Total cost from unit cost. Given unit cost (cu) = 10.5000 $/unit; quantity (Q) = 3,831 units, determine the total cost (C) in $.

Given

  • unit cost (cu) = 10.5000 $/unit

  • quantity(Q)=3,831unitsquantity (Q) = 3,831 units

Find

total cost (C), in $

Start with the thinking

  • The governing relation printed in this handbook section is Total cost from unit cost.
  • Everything except C is given, so isolate C symbolically first — never rearrange after the numbers are in.
  • Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
  • Construction Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

  1. Step 1 — State the governing relation:

    C=cu×QC = c_u \times Q

  2. Step 2 — Rearrange the relation so that C stands alone on the left-hand side.

  3. Step 3 — List the givens: unit cost (cu) = 10.5000 $/unit, quantity (Q) = 3,831 units.

  4. Step 4 — Substitute the given values into the rearranged relation.

  5. Step 5 — Evaluate:

    C=40226 $C = 40226\ \text{\$}

  6. Step 6 — Check: returning C = 40,226 $ to

    C=cu×QC = c_u \times Q

    reproduces the given quantities, and both sides carry the same units.

Answer:
C=40226 $C = 40226\ \text{\$}

Why the other options are there

  • 80,451 — kept a factor of two that cancels in the correct rearrangement.
  • 20,113 — dropped that same factor in the other direction.
  • 44,248 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Forecasting

Example 8
Total cost from unit cost — solve for unit cost (case 3) — Forecasting (8)

A construction engineering problem uses Total cost from unit cost. Given quantity (Q) = 1,683 units; total cost (C) = 36,441 $, determine the unit cost (cu) in $/unit.

Given

  • quantity(Q)=1,683unitsquantity (Q) = 1,683 units

  • total cost (C) = 36,441 $

Find

unit cost (cu), in $/unit

Start with the thinking

  • The governing relation printed in this handbook section is Total cost from unit cost.
  • Everything except cu is given, so isolate cu symbolically first — never rearrange after the numbers are in.
  • Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
  • Construction Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

  1. Step 1 — State the governing relation:

    C=cu×QC = c_u \times Q

  2. Step 2 — Rearrange the relation so that cu stands alone on the left-hand side.

  3. Step 3 — List the givens: quantity (Q) = 1,683 units, total cost (C) = 36,441 $.

  4. Step 4 — Substitute the given values into the rearranged relation.

  5. Step 5 — Evaluate:

    cu=21.6524 $/unitcu = 21.6524\ \text{\$/unit}

  6. Step 6 — Check: returning cu = 21.6524 $/unit to

    C=cu×QC = c_u \times Q

    reproduces the given quantities, and both sides carry the same units.

Answer:
cu=21.6524 $/unitcu = 21.6524\ \text{\$/unit}

Why the other options are there

  • 43.3048 — kept a factor of two that cancels in the correct rearrangement.
  • 10.8262 — dropped that same factor in the other direction.
  • 23.8176 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Forecasting

Example 9
Total cost from unit cost — solve for quantity (case 3) — Forecasting (9)

A construction engineering problem uses Total cost from unit cost. Given unit cost (cu) = 400.0 $/unit; total cost (C) = 435,908 $, determine the quantity (Q) in units.

Given

  • unit cost (cu) = 400.0 $/unit

  • total cost (C) = 435,908 $

Find

quantity (Q), in units

Start with the thinking

  • The governing relation printed in this handbook section is Total cost from unit cost.
  • Everything except Q is given, so isolate Q symbolically first — never rearrange after the numbers are in.
  • Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
  • Construction Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

  1. Step 1 — State the governing relation:

    C=cu×QC = c_u \times Q

  2. Step 2 — Rearrange the relation so that Q stands alone on the left-hand side.

  3. Step 3 — List the givens: unit cost (cu) = 400.0 $/unit, total cost (C) = 435,908 $.

  4. Step 4 — Substitute the given values into the rearranged relation.

  5. Step 5 — Evaluate:

    Q=1090 unitsQ = 1090\ \text{units}

  6. Step 6 — Check: returning Q = 1,090 units to

    C=cu×QC = c_u \times Q

    reproduces the given quantities, and both sides carry the same units.

Answer:
Q=1090 unitsQ = 1090\ \text{units}

Why the other options are there

  • 2,180 — kept a factor of two that cancels in the correct rearrangement.
  • 544.9 — dropped that same factor in the other direction.
  • 1,199 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Forecasting

Example 10
Total cost from unit cost — solve for total cost (case 4) — Forecasting (10)

A construction engineering problem uses Total cost from unit cost. Given unit cost (cu) = 87.5000 $/unit; quantity (Q) = 2,132 units, determine the total cost (C) in $.

Given

  • unit cost (cu) = 87.5000 $/unit

  • quantity(Q)=2,132unitsquantity (Q) = 2,132 units

Find

total cost (C), in $

Start with the thinking

  • The governing relation printed in this handbook section is Total cost from unit cost.
  • Everything except C is given, so isolate C symbolically first — never rearrange after the numbers are in.
  • Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
  • Construction Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

  1. Step 1 — State the governing relation:

    C=cu×QC = c_u \times Q

  2. Step 2 — Rearrange the relation so that C stands alone on the left-hand side.

  3. Step 3 — List the givens: unit cost (cu) = 87.5000 $/unit, quantity (Q) = 2,132 units.

  4. Step 4 — Substitute the given values into the rearranged relation.

  5. Step 5 — Evaluate:

    C=186550 $C = 186550\ \text{\$}

  6. Step 6 — Check: returning C = 186,550 $ to

    C=cu×QC = c_u \times Q

    reproduces the given quantities, and both sides carry the same units.

Answer:
C=186550 $C = 186550\ \text{\$}

Why the other options are there

  • 373,100 — kept a factor of two that cancels in the correct rearrangement.
  • 93,275 — dropped that same factor in the other direction.
  • 205,205 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Forecasting

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