Problem 4: (18 marks) Consider the following equations, where q denotes quantity

Question

Problem 4: (18 marks) Consider the following equations, where q denotes quantity in kilograms, p denotes price in dollars and yrc denotes total cost in dollars: q 25,000-100p y-c = 250,000 + 55q a. Express total revenue TR) as a function of p. b. Express total cost (rc) as a function of p. c. Express profit (n) as a function of p. d. Determine the break-even level(s) of production. e. (1 mark) (1 mark) (2 marks) (6 marks) Determine the profit maximising level of production. Find the price, total revenue, (5 marks) total cost and profit at this profit maximising level of production. Graph the profit function in the region p intercepts f. 0, 0 . Label all vertices and (3 marks)

Explanation / Answer

a. TR = P*Q = 25000p - 100p2

b. TC = 250000 + 55(25000 - 100p)

TC = 250000 + 1375000 - 5500p

TC = 1625000 - 5500p

c. Profit = TR - TC

Pr = 25000p - 100p2 - (1625000 - 5500p)

Pr = -1625000 - 100p2 + 30500p

d. Break Even Level is the point where Total Cost equals total revenue.

25000p - 100p2 = 1625000 - 5500p

1625000 + 100p2 - 30500p = 0

p = 68.79

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