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Productivity and Unit Cost

Productivity measures output per unit of resource (m³ poured per hour, m² formed per day). Unit cost is the total cost to produce one unit of output (cost per m³, per m of excavation). To find how long a job takes, divide total quantity by productivity. To find cost, multiply unit cost by quantity. Watch units carefully — a crew's productivity is different from one worker's productivity. Manhours = number of workers × hours worked, a measure of labor input regardless of schedule. If you know output and manhour requirement, you can find crew size or duration.

$$\text{Duration}=\frac{\text{Total Quantity}}{\text{Productivity}}, \qquad \text{Unit Cost}=\frac{\text{Total Cost}}{\text{Total Output}}$$
$$\text{Manhours}=\text{Workers}\times\text{Hours}, \qquad \text{Productivity}_{\text{crew}}=\frac{\text{Output}}{\text{Manhours}}$$

Formwork Crew Duration

A crew installs 120 square meters of formwork in 10 hours. How long will the same crew need for 360 square meters?

$$\text{Productivity}=\frac{120}{10}=12\text{ m}^2/\text{hr}$$
$$t=\frac{360}{12}=30\text{ hr}$$

Final answer: 30 hours.

★ Unit Cost from Labor and Output

A masonry crew of 5 workers earns P800/worker-day. They can lay 15 m² of masonry per day. Find the unit cost of masonry per square meter.

Total labor cost per day = 5 workers × P800 = P4,000/day. Output = 15 m²/day.

$$\text{Unit Cost}=\frac{\text{Cost per day}}{\text{Output per day}}=\frac{4000}{15}=\text{P}266.67\text{ per m}^2$$

Final answer: P266.67 per m².

★★ Manhours Required

A concrete pouring job requires 240 manhours. If a crew of 8 workers works 10-hour days, how many days will the job take?

The crew produces 8 workers × 10 hrs/day = 80 manhours/day.

$$\text{Days}=\frac{240\text{ manhours}}{80\text{ manhours/day}}=3\text{ days}$$

Final answer: 3 days.

★★ Determining Crew Size for a Deadline

An excavation of 500 m³ must be completed in 5 days. One crew member excavates 4 m³ per 8-hour day. How many workers are needed? Work is done 8 hours per day.

Total output needed = 500 m³ in 5 days = 100 m³/day. Each worker outputs 4 m³/day.

$$n=\frac{100\text{ m}^3/\text{day}}{4\text{ m}^3/\text{worker-day}}=25\text{ workers}$$

Final answer: 25 workers are needed.

★★★ Combined Crew Output and Cost Comparison

Crew A can do a job in 10 days at P15,000/day. Crew B can do the same job in 15 days at P9,000/day. If both crews work together, how long will the job take and which is the cheaper option: both crews working together vs. just Crew A alone?

Work rates: A does 1/10 job/day; B does 1/15 job/day.

$$\text{Combined rate}=\frac{1}{10}+\frac{1}{15}=\frac{3+2}{30}=\frac{1}{6}\text{ job/day}$$

Together: 6 days, at a daily cost of P15,000+P9,000 = P24,000.

$$\text{Cost together}=6\times24{,}000=\text{P}144{,}000$$
$$\text{Cost A alone}=10\times15{,}000=\text{P}150{,}000$$

Final answer: Together takes 6 days costing P144,000, which is P6,000 cheaper than Crew A alone. Use both crews together.

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