Given the following cubic cost function: C=2Q^3-3Q^2+5Q+12,

Linear Demand Function:Q(d) = 30-2P

Contraints

a=2>0

b=-3<0

c=5>0

d=12>0

R=15Q-(1/2)Q^2, profit(pie symbol)Q=-2Q^3+5/2Q^2+10Q-12

via --------->[9.4.5] profit(0)=0 profit"(Q)=-12Q+5--->concave when Q>5/12

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*