A construction engineering problem uses Crew productivity. Given production rate (P) = 9.0000 units/hr; duration (t) = 159.0 hr, determine the total quantity (Q) in units.

Start with the thinking

• The governing relation printed in this handbook section is Crew productivity.
• 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:

   $$Q = P \times t$$

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

3. Step 3

   $$List the givens: production rate (P) = 9.0000 units/hr, duration (t) = 159.0 hr$$

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

5. Step 5 — Evaluate:

   $$Q = 1431\ \text{units}$$

6. Step 6 — Check: returning Q = 1,431 units to

   $$Q = P \times t$$

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

Why the other options are there

• 2,862 — kept a factor of two that cancels in the correct rearrangement.
• 715.5 — dropped that same factor in the other direction.
• 1,574 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Indices

A construction engineering problem uses Total cost from unit cost. Given unit cost (cu) = 123.5 $/unit; quantity (Q) = 7,247 units, determine the 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:

   $$C = c_u \times Q$$

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) = 123.5 $/unit, quantity (Q) = 7,247 units.

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

5. Step 5 — Evaluate:

   $$C = 895005\ \text{\$}$$

6. Step 6 — Check: returning C = 895,005 $ to

   $$C = c_u \times Q$$

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

Why the other options are there

• 1,790,009 — kept a factor of two that cancels in the correct rearrangement.
• 447,502 — dropped that same factor in the other direction.
• 984,505 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Indices

earned value cost performance index for a highway construction contract Given earned value (BCWP) (EV) = 29,000 $; actual cost (ACWP) (AC) = 85,000 $; cost variance (CV) = -100,000 $, determine the cost performance index (CPI).

Start with the thinking

• The governing relation printed in this handbook section is Earned value: cost performance index and cost variance.
• Everything except CPI is given, so isolate CPI 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.
• Earned value management measures project cost performance and productivity using cost performance index and cost variance.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$CPI = \dfrac{EV}{AC}, \qquad CV = EV - AC$$

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

3. Step 3 — List the givens: earned value (BCWP) (EV) = 29,000 $, actual cost (ACWP) (AC) = 85,000 $, cost variance (CV) = -100,000 $.

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

5. Step 5 — Evaluate:

   $$CPI = 0.3412$$

6. Step 6 — Check: returning CPI = 0.3412 to

   $$CPI = \dfrac{EV}{AC}, \qquad CV = EV - AC$$

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

Why the other options are there

• 0.6824 — kept a factor of two that cancels in the correct rearrangement.
• 0.1706 — dropped that same factor in the other direction.
• 0.3753 — rounded an intermediate value before the final step.

Reference: FE Handbook — Nomenclature (earned value / productivity)

A construction engineering problem uses Crew productivity. Given duration (t) = 132.0 hr; total quantity (Q) = 223.0 units, determine the production rate (P) in units/hr.

Start with the thinking

• The governing relation printed in this handbook section is Crew productivity.
• Everything except P is given, so isolate P 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:

   $$Q = P \times t$$

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

3. Step 3

   $$List the givens: duration (t) = 132.0 hr, total quantity (Q) = 223.0 units$$

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

5. Step 5 — Evaluate:

   $$P = 1.6894\ \text{units/hr}$$

6. Step 6 — Check: returning P = 1.6894 units/hr to

   $$Q = P \times t$$

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

Why the other options are there

• 3.3788 — kept a factor of two that cancels in the correct rearrangement.
• 0.8447 — dropped that same factor in the other direction.
• 1.8583 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Indices

A construction engineering problem uses Total cost from unit cost. Given quantity (Q) = 9,647 units; total cost (C) = 21,314 $, determine the 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:

   $$C = c_u \times Q$$

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

3. Step 3 — List the givens: quantity (Q) = 9,647 units, total cost (C) = 21,314 $.

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

5. Step 5 — Evaluate:

   $$cu = 2.2094\ \text{\$/unit}$$

6. Step 6 — Check: returning cu = 2.2094 $/unit to

   $$C = c_u \times Q$$

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

Why the other options are there

• 4.4188 — kept a factor of two that cancels in the correct rearrangement.
• 1.1047 — dropped that same factor in the other direction.
• 2.4303 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Indices

earned value analysis to assess cost performance on a construction project Given earned value (BCWP) (EV) = 174,500 $; actual cost (ACWP) (AC) = 398,500 $; cost performance index (CPI) = 0.8800, determine the cost variance (CV) in $.

Start with the thinking

• The governing relation printed in this handbook section is Earned value: cost performance index and cost variance.
• Everything except CV is given, so isolate CV 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.
• Earned value management measures project cost performance and productivity using cost performance index and cost variance.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$CPI = \dfrac{EV}{AC}, \qquad CV = EV - AC$$

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

3. Step 3 — List the givens: earned value (BCWP) (EV) = 174,500 $, actual cost (ACWP) (AC) = 398,500 $, cost performance index (CPI) = 0.8800.

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

5. Step 5 — Evaluate:

   $$CV = -224000\ \text{\$}$$

6. Step 6 — Check: returning CV = -224,000 $ to

   $$CPI = \dfrac{EV}{AC}, \qquad CV = EV - AC$$

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

Why the other options are there

• -448,000 — kept a factor of two that cancels in the correct rearrangement.
• -112,000 — dropped that same factor in the other direction.
• -246,400 — rounded an intermediate value before the final step.

Reference: FE Handbook — Nomenclature (earned value / productivity)

A construction engineering problem uses Crew productivity. Given production rate (P) = 19.0000 units/hr; total quantity (Q) = 657.0 units, determine the duration (t) in hr.

Start with the thinking

• The governing relation printed in this handbook section is Crew productivity.
• Everything except t is given, so isolate t 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:

   $$Q = P \times t$$

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

3. Step 3 — List the givens: production rate (P) = 19.0000 units/hr, total quantity (Q) = 657.0 units.

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

5. Step 5 — Evaluate:

   $$t = 34.5789\ \text{hr}$$

6. Step 6 — Check: returning t = 34.5789 hr to

   $$Q = P \times t$$

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

Why the other options are there

• 69.1579 — kept a factor of two that cancels in the correct rearrangement.
• 17.2895 — dropped that same factor in the other direction.
• 38.0368 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Indices

A construction engineering problem uses Total cost from unit cost. Given unit cost (cu) = 50.5000 $/unit; total cost (C) = 127,360 $, determine the 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:

   $$C = c_u \times Q$$

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) = 50.5000 $/unit, total cost (C) = 127,360 $.

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

5. Step 5 — Evaluate:

   $$Q = 2522\ \text{units}$$

6. Step 6 — Check: returning Q = 2,522 units to

   $$C = c_u \times Q$$

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

Why the other options are there

• 5,044 — kept a factor of two that cancels in the correct rearrangement.
• 1,261 — dropped that same factor in the other direction.
• 2,774 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Indices

productivity and cost variance tracking on a building project schedule Given earned value (BCWP) (EV) = 160,000 $; cost performance index (CPI) = 0.5200; cost variance (CV) = 38,000 $, determine the actual cost (ACWP) (AC) in $.

Start with the thinking

• The governing relation printed in this handbook section is Earned value: cost performance index and cost variance.
• Everything except AC is given, so isolate AC 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.
• Earned value management measures project cost performance and productivity using cost performance index and cost variance.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$CPI = \dfrac{EV}{AC}, \qquad CV = EV - AC$$

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

3. Step 3 — List the givens: earned value (BCWP) (EV) = 160,000 $, cost performance index (CPI) = 0.5200, cost variance (CV) = 38,000 $.

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

5. Step 5 — Evaluate:

   $$AC = 307692\ \text{\$}$$

6. Step 6 — Check: returning AC = 307,692 $ to

   $$CPI = \dfrac{EV}{AC}, \qquad CV = EV - AC$$

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

Why the other options are there

• 615,385 — kept a factor of two that cancels in the correct rearrangement.
• 153,846 — dropped that same factor in the other direction.
• 338,462 — rounded an intermediate value before the final step.

Reference: FE Handbook — Nomenclature (earned value / productivity)

A construction engineering problem uses Crew productivity. Given production rate (P) = 18.0000 units/hr; duration (t) = 168.0 hr, determine the total quantity (Q) in units.

Start with the thinking

• The governing relation printed in this handbook section is Crew productivity.
• 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:

   $$Q = P \times t$$

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

3. Step 3

   $$List the givens: production rate (P) = 18.0000 units/hr, duration (t) = 168.0 hr$$

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

5. Step 5 — Evaluate:

   $$Q = 3024\ \text{units}$$

6. Step 6 — Check: returning Q = 3,024 units to

   $$Q = P \times t$$

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

Why the other options are there

• 6,048 — kept a factor of two that cancels in the correct rearrangement.
• 1,512 — dropped that same factor in the other direction.
• 3,326 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Indices