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.

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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.

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