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.
(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?
(ii) At what level of weekly sales would company B maximize its profits? (4
(iii) If the two companies merge into one, what would be the profit maximizing
output per week and what would be the weekly profit?