Question

If fixed costs are 30, variable costs per unit are Q + 3 and the demand function is

Answer 1

The maximum profit is 154

Total cost is the sum of the fixed cost and variable cost.

Let us assume that Q units are produced, hence:

Fixed cost = 30, variable cost = Q * (Q + 3) = Q² + 3Q

Total cost = Fixed cost + variable cost = 30 + (Q² + 3Q) = Q² + 3Q + 30

Given the demand function:

P + 2Q = 50

P = 50 - 2Q

Therefore the Revenue (R) = P * Q = (50 - 2Q) * (Q) = 50Q - 2Q²

The profit is the difference between the revenue and the cost, hence:

profit (p) = revenue - cost = (50Q - 2Q²) - (Q² + 3Q + 30) = -3Q² + 47Q - 30

p = -3Q² + 47Q - 30

At break even, the revenue is equal to the cost, hence no profit. At breakeven:

revenue = cost

50Q - 2Q² = Q² + 3Q + 30

3Q² - 47Q + 30 = 0

Q = 0.6 or 15

At breakeven the number of units produced are 0.6 and 15

The maximum profit is at dp/dQ = 0

p = -3Q² + 47Q - 30

dp/dQ = -6Q + 47 = 0

6Q = 47

Q = 7,83

p = -3(7.83)² + 47(7.83) - 30 = 154

Therefore the maximum profit is 154

Find out more at: brainly.com/question/17200182