Company A sells all its output to company B for Sh. 200 per unit. The cost of
the sales per week in company A are given by the function C = 2q2
+ 40q + 80
where q is the value of weekly sales. Company B uses the output of company
A to manufacture a product whose demand is dependent on the sale price. The
revenue per week of company B is given by the function:
R = 1000q – 16q2
and the cost per week of company B excluding cost of the
products bought from company A are given by the function.
C = 2q2
+ 80q + 400
Company A can restrict the weekly supply of its product to company B, but
cannot raise the unit price above Sh. 200. The two companies are considering
whether to merge together into a single company.
Required:
(i) At what weekly sales would company A maximize its profits? What would be
the profit or loss of company B if company A were able to supply a profit
maximizing quantity of its product each week?
(7 marks)
(ii) At what level of weekly sales would company B maximize its profits? (4
marks)
(iii) If the two companies merge into one, what would be the profit maximizing
output per week and what would be the weekly profit?
(4 marks)