A construction engineering problem uses Crew productivity. Given production rate (P) = 41.0000 units/hr; duration (t) = 120.0 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

   $$List the givens: production rate (P) = 41.0000 units/hr, duration (t) = 120.0 hr$$

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

5. Step 5 — Evaluate:

   $$Q = 4920\ \text{units}$$

6. Step 6 — Check: returning Q = 4,920 units to

   $$Q = P \times t$$

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

Why the other options are there

• 9,840 — kept a factor of two that cancels in the correct rearrangement.
• 2,460 — dropped that same factor in the other direction.
• 5,412 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Variances

A construction engineering problem uses Total cost from unit cost. Given unit cost (cu) = 96.5000 $/unit; quantity (Q) = 3,603 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) = 96.5000 $/unit, quantity (Q) = 3,603 units.

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

5. Step 5 — Evaluate:

   $$C = 347690\ \text{\$}$$

6. Step 6 — Check: returning C = 347,690 $ to

   $$C = c_u \times Q$$

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

Why the other options are there

• 695,379 — kept a factor of two that cancels in the correct rearrangement.
• 173,845 — dropped that same factor in the other direction.
• 382,458 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Variances

earned value cost performance index for a highway construction contract Given earned value (BCWP) (EV) = 247,500 $; actual cost (ACWP) (AC) = 440,000 $; cost variance (CV) = 85,500 $, 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) = 247,500 $, actual cost (ACWP) (AC) = 440,000 $, cost variance (CV) = 85,500 $.

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

5. Step 5 — Evaluate:

   $$CPI = 0.5625$$

6. Step 6 — Check: returning CPI = 0.5625 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

• 1.1250 — kept a factor of two that cancels in the correct rearrangement.
• 0.2813 — dropped that same factor in the other direction.
• 0.6188 — 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) = 185.0 hr; total quantity (Q) = 1,706 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

   $$List the givens: duration (t) = 185.0 hr, total quantity (Q) = 1,706 units$$

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

5. Step 5 — Evaluate:

   $$P = 9.2216\ \text{units/hr}$$

6. Step 6 — Check: returning P = 9.2216 units/hr to

   $$Q = P \times t$$

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

Why the other options are there

• 18.4432 — kept a factor of two that cancels in the correct rearrangement.
• 4.6108 — dropped that same factor in the other direction.
• 10.1438 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Variances

A construction engineering problem uses Total cost from unit cost. Given quantity (Q) = 762.0 units; total cost (C) = 148,123 $, 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) = 762.0 units, total cost (C) = 148,123 $.

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

5. Step 5 — Evaluate:

   $$cu = 194.4\ \text{\$/unit}$$

6. Step 6 — Check: returning cu = 194.4 $/unit to

   $$C = c_u \times Q$$

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

Why the other options are there

• 388.8 — kept a factor of two that cancels in the correct rearrangement.
• 97.1936 — dropped that same factor in the other direction.
• 213.8 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Variances

earned value analysis to assess cost performance on a construction project Given earned value (BCWP) (EV) = 82,000 $; actual cost (ACWP) (AC) = 416,500 $; cost performance index (CPI) = 1.3600, 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) = 82,000 $, actual cost (ACWP) (AC) = 416,500 $, cost performance index (CPI) = 1.3600.

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

5. Step 5 — Evaluate:

   $$CV = -334500\ \text{\$}$$

6. Step 6 — Check: returning CV = -334,500 $ 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

• -669,000 — kept a factor of two that cancels in the correct rearrangement.
• -167,250 — dropped that same factor in the other direction.
• -367,950 — 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) = 71.0000 units/hr; total quantity (Q) = 3,710 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) = 71.0000 units/hr, total quantity (Q) = 3,710 units.

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

5. Step 5 — Evaluate:

   $$t = 52.2535\ \text{hr}$$

6. Step 6 — Check: returning t = 52.2535 hr to

   $$Q = P \times t$$

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

Why the other options are there

• 104.5 — kept a factor of two that cancels in the correct rearrangement.
• 26.1268 — dropped that same factor in the other direction.
• 57.4789 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Variances

A construction engineering problem uses Total cost from unit cost. Given unit cost (cu) = 274.0 $/unit; total cost (C) = 195,376 $, 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) = 274.0 $/unit, total cost (C) = 195,376 $.

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

5. Step 5 — Evaluate:

   $$Q = 713.1\ \text{units}$$

6. Step 6 — Check: returning Q = 713.1 units to

   $$C = c_u \times Q$$

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

Why the other options are there

• 1,426 — kept a factor of two that cancels in the correct rearrangement.
• 356.5 — dropped that same factor in the other direction.
• 784.4 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Variances

productivity and cost variance tracking on a building project schedule Given earned value (BCWP) (EV) = 323,500 $; cost performance index (CPI) = 0.7100; cost variance (CV) = 69,500 $, 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) = 323,500 $, cost performance index (CPI) = 0.7100, cost variance (CV) = 69,500 $.

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

5. Step 5 — Evaluate:

   $$AC = 455634\ \text{\$}$$

6. Step 6 — Check: returning AC = 455,634 $ 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

• 911,268 — kept a factor of two that cancels in the correct rearrangement.
• 227,817 — dropped that same factor in the other direction.
• 501,197 — 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) = 59.0000 units/hr; duration (t) = 29.0000 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

   $$List the givens: production rate (P) = 59.0000 units/hr, duration (t) = 29.0000 hr$$

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

5. Step 5 — Evaluate:

   $$Q = 1711\ \text{units}$$

6. Step 6 — Check: returning Q = 1,711 units to

   $$Q = P \times t$$

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

Why the other options are there

• 3,422 — kept a factor of two that cancels in the correct rearrangement.
• 855.5 — dropped that same factor in the other direction.
• 1,882 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Variances