Given the following cubic cost function: TC(Q)=0.1Q^3-2Q^2+50Q+100,

where VC=0.1Q^3-2Q^2+50Q,

where MC=0.3Q^2-4Q+50,

where ATC=0.1Q^2-2Q+50+ 100,

Q

where AVC= 0.1Q^3-2Q^2+50Q

Q

=0.1Q^2-2Q+50

And given the following demand function and constraints:

1)Linear Demand Function:Q(d) = -0.005x+ 27.5

2) Constraints:

If 20 units will be produce,

2) a. Total cost = 1,100

b. Variable cost = 1,000

c. Marginal cost = 90

d. Average Variable Cost = 50

Task: What would be a quadratic profit function that maximizes profit using the following assumptions. Show work.

1. If nothing is produced, the profit will be negative because of fixed costs

2.The profit function is strictly concave

3.The maximum profit occurs at a positive output level Q*