Answer to Question #253628 in Microeconomics for Khushi

Question

two sub-companies A and B produce cars, they work out their daily profit (p) based on the following formulas; Company A: p=-2c² + 26c – 60 Where p is the profit in 1,000 of pounds and c is the number of cars produced per day. Top management are interested in the following issues: Company B: p=-c' + 9c² – 60 i) Sketch the graph of company A's profit p for c in the range 0 to 13 and company B's profit p for c in the range 0 to 9, on the same graph. ii) Within what values of c does company A make a profit? iii) For what numbers of cars produced does each company make their largest profit? iv) Between what values of c does company B make a larger profit than company A? v) What value of c gives the largest difference in the profits of the two companies, WITHIN the interval found in part iv) of this question?

Answer 1

i

i

The above table shows the profit of company A, y represents profit earned and x represents the number of cars produced. 

The above table represents profits and the number of cars produced for company B. 

To get these tables, substitute the values for c and compute p. 

ii

Company A makes a profit for c>2, we can see that at c = 2 company A has zero profit and below c = 2, the company incurred losses, so above c = 2 ( 3 to 13) company makes profits.

 When c= 13, A makes the largest profit, and for B when c = 9 they make the largest profit. 

For the largest profit, A should produce 13 cars and B should produce 9 cars. 

iii

The curves intersect at x = 3.6, so above c = 3.6 or rounds to 4, company B makes more profit than company A. 

As from above table for company B at c = 9 has got 678000 pounds. Company A at c = 9 got 360000 pounds.

Note: p is given in thousand pounds, so we need to convert our values into thousand pounds.

So the difference = 678000-360000 = 318000 pounds. Largest difference occur at c = 9. 

For company B, between the interval c = 3.6 and 9 makes profits than company A.