The nation of ectenia has 40 competitive apple orchards, which sell apples at the world price of $2 per apple. the following equations describe the production function and the marginal product of labor in each orchard: q = 120l−l2, mpl = 120−2l where q is the number of apples produced in a day, l is the number of workers, and mpl is the marginal product of labor. what is each orchard’s labor demand as a function of the daily wage w?

(a) l=60−0.25w
(b) l=2,400−10w
(c) l=120−2w
(d) l=60−0.5w

d. 70%

Explanation:

It is best that the Operating point be around 70%.

The Operating Point is the ratio between the Number of Customers served per period (Mean Service Rate) to the number of customer Arrival per period (Mean Arrival Rate).

As the text says, it is better that Mean Service Rate exceed the Mean Arrival Rate and that the Mean Arrival Rate should not get too close to the Mean Service Rate. This makes 70% the best choice as Mean Arrival Rate is both less than and not too close to the Mean Service Rate.

Also, it would be better to have the Mean Service Rate at 70% because it would keep the servers/ waiters enough work to do but at the same time they can cater to new arrivals efficiently. If the Mean Arrival Rate was more than the Mean Service Rate, more people would be arriving than the Servers can serve. This can lead to mistakes and neglect of customers.

For these reasons, 70% is the best option.

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