A pizzeria produces 3,000 pizzas during its first week of operation using 10 drums of marinara sauce, 150 hours of labor, and 50 therms of energy. Pizzas sell for $15 each, and workers are paid $18 per hour. The marinara sauce costs $200 per drum, and the energy cost is $7 per therm. During its second week of operation, it produces 2,900 pizzas using only 140 hours of labor. All costs and prices are constant from the first to second week. What has been the change in their labor productivity?单项选择题
A
Productivity has increased by 5.3%.
B
Productivity has decreased by 5.3%.
C
Productivity has increased by 3.6%.
D
Productivity has decreased by 3.6%.

Question

A pizzeria produces 3,000 pizzas during its first week of operation using 10 drums of marinara sauce, 150 hours of labor, and 50 therms of energy. Pizzas sell for $15 each, and workers are paid $18 per hour. The marinara sauce costs $200 per drum, and the energy cost is $7 per therm. During its second week of operation, it produces 2,900 pizzas using only 140 hours of labor. All costs and prices are constant from the first to second week. What has been the change in their labor productivity?单项选择题

A

Productivity has increased by 5.3%.

B

Productivity has decreased by 5.3%.

C

Productivity has increased by 3.6%.

D

Productivity has decreased by 3.6%.

BlackTom AI · Accepted Answer

The question asks for the change in labor productivity from Week 1 to Week 2, where labor productivity is defined as pizzas produced per hour of labor.
First, compute Week 1 productivity: 3,000 pizzas produced using 150 hours of labor. 3,000 / 150 = 20 pizzas per hour.
Next, compute Week 2 productivity: 2,900 pizzas produced using 140 hours of labor. 2,900 / 140 ≈ 20.7143 pizzas per hour.
Now determine the change in productivity: (Week 2 productivity − Week 1 productivity) / Week 1 productivity = (20.7143 − 20) / 20 ≈ 0.7143 / 20 ≈ 0.035714, which is about 3.57%.
With that in mind, evaluate each option:
- Option A: Productivity has increased by 5.3%. This overstates the improvement; the calculated increase is about 3.57%, not 5.3%, so this is incorrect.
- Option B: Productivity has decreased by 5.3%. The productivity actually rose, not fell, and the magnitude is not 5.3%, so this is incorrect.
- Option C: Productivity has increased by 3.6%. This matches the approximate 3.57% increase derived from the numbers, so this is the correct magnitude and direction.
- Option D: Productivity has decreased by 3.6%. This contradicts the actual increase we computed, since Week 2 productivity is higher, not lower, making this option incorrect.
Note that the key idea is comparing output per hour between the two weeks; any option that misstates the direction (increase vs. decrease) or the percent magnitude is inaccurate.

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