Question

A firm has analyzed its operating conditions, prices, and cost have developed the following functions: R = 400 – 4q2 (per thousand naira) and Cost = q2 + 10q + 30 (per thousand naira) where q is the number of units produced and sold. If the firm wishes to maximize profit:

(a) What quantity should be sold and at what price?

(b) What will be the amount of profit?

2. Find the point of maximum value of the revenue function given as P = 400 – 4q. Hence, find the revenue.

Answer 1

1.

(a) $R= 400-4Q^2$

$MR=8Q$

$C=Q^2+10Q+30$

$MC=2Q+10$

At maximum profit:

$MR=MC$

$8Q=2Q+10$

$Q= 1.66667$

Q is approximately =2

(b)

$R=400-4(4)=384$

$C=4+20+30=54$

Profit$= 384-54=330$

2.

$P=400-4Q$

Max value of revenue is 4

Revenue $= 400-4(4)=384$