Question

Please show the work

1. Smith Company produces and sells racquet balls. Its total revenue is given as

TR = 1,000Q – 0.1Q²

The company has estimated a functional relationship between total output produced and the total cost. The annual cost of producing racquet balls in dollars is:

                                                    

                                     TC = 40,000 - 200Q + 0.4Q²

1. Determine the profit maximizing level of output.

2. What is the level of maximum profit?

                       

Answer 1

(a) Profit is miximized where Marginal revenue is equal to Marginal cost.

First we will calculate the marginal revenue and marginal cost by differentiation as per below:

Marginal revenue (dTR/ dQ) = 1000 - 0.2Q

Marginal cost (dTC / dQ) = -200 + 0.8Q

Now, we will equate MR and MC as per below:

1000 - 0.2Q = -200 + 0.8Q

1000 + 200 = 0.8Q + 0.2Q

1200 = Q

So, profit maximizing output is 1200 units.

(b) Profit is given by:

Profit = Total revenue (TR) - Total cost (TC)

Profit = 1000 Q- 0.1Q² - 40000 + 200Q - 0.4Q²

Profit = -40000 + 1200 Q - 0.5Q²

Now, for maximum profit, we will put the value of Q = 1200 in the above equation as below,

Profit = -40000 + 1200 (1200) - 0.5 (1200)²

Profit = - 40000 + 1440000 - 720000

Profit = 680000

So, maximum profit = 680000