Answer Happy

A bakery mass produces 4 different types of cake: carrot, chocolate, vanilla, and angel-food. The bakery measures cake characteristics using two different features: sweetness (S) and density (D). The following table summarizes the characteristics of each type of cake as well as the (max) num- ber of each type that are baked each month: Cake Carrot 100 15 Chocolate 90 18 Vanilla 86 6 Angel food 110 3 Market The cakes can either be sold directly from the bakery at \$14 a cake or sold at a local market at a higher rate. There are two markets - A and B - that have requirements for average sweetness and density of cakes sold there. No more than 7 cakes can be sold at each market. The table below summarizes these requirements and gives the selling price per cake at each market: SD Max baked 3810 2700 4000 1500 S A at least 98 B at least 100 D at most 10 at most 8 Max cakes Price per cake (dollars) 20 30 7 7 The S and D values for each market are calculated as the weighted averages of the S and D of the cakes sold at the market. (a) Formulate a linear program that will yield the largest possible revenue for the bakery. As- sume it is okay to sell fractional cakes, since we are planning in aggregate. 1 (b) Build and solve the problem in Julia. What are the optimal numbers of each type of cake that the bakery should sell directly and at each market?