Question

Sharon is opening a new pizza restaurant that will use a combination of workers and ovens to produce pizzas. Sharon knows from experience that the total number of pizzas she can produce in an hour is given by the function q=4K0.5L0.5 , where q is the number of pizzas per hour, K is the number of ovens, and L is the number of workers. Suppose another pizza restaurant in the same town can produce 19 pizzas per hour. Being an extremely competitive person, Sharon wants to produce 20 pizzas per hour. Therefore, his total hourly cost function is given by ____

Answer 1

Q+X = [4K^1/2L^1/2] + X

Step-by-step explanation:

L = labour = workers

K = capital = ovens

You don't have the exact value of Q since the values of K and L are not given.

You should however note that Q is less than or equal to 19 pizzas/hour, since Sharon sought to stretch his capacity by producing up to 20 pizzas/hour owing to the presence of a competitor.

Assuming the distance/difference between 20 and Q is X (a positive number).

Sharon's new hourly cost function will be:

`Q+X = [4K^1/2L^1/2] + X`

Q+X = 20 and the law of mathematics states that whatever you add to the left hand side must be added to the right hand side, hence the addition of X to both sides of the equation instead of the left hand side alone.

The function can now be rewritten as 20 = [4K^1/2L^1/2] + X

where X = 20 - Q