The Frisbee Pie company can make pie tins for bakeries, which are willing to pay
($40 - $2.45*Q1) per dozen, where Q1 is the number of dozens of pie tins. But the fraternities and sororities at the nearby university are willing to pay ($38 - $3.05*Q2) per dozen, where Q2 is the number of dozens of pie tins {to be used to throw around the front lawns of their houses}. It costs ($22 + $2.65*Q) to produce Q dozen tins. Management wants to maximize profit (i.e., revenue minus cost).
Write out the complete algebraic formulation (decision variables, objective function, constraints).
5a. How many dozen (fractions are allowed) should be made for sale to the bakeries?
5b. What price per dozen should be charged for the ones sold to the bakeries?
5c. How many dozen (fractions are allowed) should be made for sale to the fraternities/sororities?
5d. What price per dozen should be charged for the ones sold to the fraternities/sororities?
5e. What is the total profit?