Miko's Bakery is a pie shop that specializes in custard and fruit pies. It makes delicious pies and sells them at reasonable prices so that it can sell all the pies it makes in a day. Every dozen custard pies net Miko's $15 and requires 12 pounds of flour, 50 eggs, 5 pounds of sugar, and no fruit mixture. Every dozen fruit pies nets a $25 profit and uses 10 pounds of flour, 40 eggs, 10 pounds of sugar, and 15 pounds of fruit mixture. On a given day, Miko's found that they had 150 pounds of flour, 500 eggs, 90 pounds of sugar, and 120 pounds of fruit mixture available. Formulate and solve a linear program that will give the optimal production mix for this day at Miko's.
a) Suppose Miko's found that 10% of its fruit mixture had been stored in containers that were not air-tight. For quality and health reasons, he decided to not use any of this portion of the mixture. How would this affect the optimal production schedule? Explain.
b) What is binding under the current production schedule?
c) How much would profit increase for each additional egg acquired and how much would it go down for each additional egg lost? What range would this apply to (range of feasibility)?
d) Miko's has in the past made a third type of pie, a chocolate pie. Given the current prices of ingredients, Miko's estimates that it would net a profit of $27 per dozen chocolate pies. Each dozen chocolate pies requires 15 pounds of flour, 30 eggs, 12 pounds of sugar and no fruit mixture. Reformulate and resolve the model with this new information. Would it be profitable to make any chocolate pies? Analyze the reduced cost for chocolate pies to explain why we are not making any.