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In: Statistics and Probability

The Pat-A-Cake Pastry Shop makes chocolate cake in three sizes – Small, Medium, and Large. For...

The Pat-A-Cake Pastry Shop makes chocolate cake in three sizes – Small, Medium, and Large. For each size, the number of cakes made is an integer (i.e. the shop does not bake only half of a cake). The shop has the following amounts of the three main ingredients on hand – 400 ounces of cake flour, 550 ounces of caster sugar, and 150 ounces of cocoa powder. The table below provides details on the amount of each ingredient required for each cake size as well as the profit contributions. The shop wants to make the appropriate amount of each cake size in order to maximize profit. Cake Small Medium Large Available Plain flour (Ounce) 8 16 21 400 Caster sugar (Ounce) 18 22 25 550 Cocoa powder (Ounce) 3 5 11 150 Profit/Unit $18 $25 $32

a. Develop a spreadsheet model and find the optimal solution using Excel Solver. What is the optimal total profit? Enter your answer without a dollar sign.

b. Based on your answer for a., what quantity of large cakes should be produced to maximize profit contribution? Remember that the number of cakes made should be an integer.

c. Based on your answer for a., what quantity of medium cakes should be produced to maximize profit contribution? Remember that the number of cakes should be an integer.

d. Based on your answer for a., what quantity of small cakes should be produced to maximize profit contribution? Remember that the number of cakes should be an integer.

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orchestra answered 1 year ago
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