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Question

Demand and cost equation.

q = quantity in kg

p = price in $

c = total costs in $

p = 350 - 68q

c = 265 + 70q

a. Break-even level(s) of production to four decimal places.

b. Profit maximising level of production to four decimal places.

I determined that the variable cost = p(350), the fixed cost = c(265) and of course q = to kg.

Answer 1

Revenue: R = qp = 350q - 68q²;

a) Equilibrium: R = c; 350q - 68q² = 265 + 70q; 68q² - 280q + 265 = 0; q = (140 ±√1580)/68; q = 2.6434 kg

or q = 1.4743 kg; so we have 2 break-even

b) Profit P = R - c = - 68q² + 280q - 265; dP/dq = - 136q + 280 = 0; q = 280/136 = 2.0588 kg is production level maximaising profit because P'' = - 136 < 0.