Question

Optimized Cookie Production for a BCS Party. A friend was bringing small bags of cookies to sell at a fairly large BCS Championship Game Watch Party (there were no TCU fans present, however). Three kinds of cookies were sold: Stars (sold for $1 per bag), Circles (sold for $0.75 per bag), and Stars and Stripes (sold for $1.50 per bag). He was to bring the cookies to the Watch Party in three large boxes. (The boxes did not have to be full, but he could not bring more than three large boxes of cookies). By volume, it is a known fact that one of the large boxes can hold 100 bags of Stars, 120 bags of Circles, or 80 bags of Stars and Stripes (or a corresponding mix of cookies). HINT: Don’t concern yourself with what each box held; view this as an aggregate limit in the numbers of cookies. Previous parties had given him some hints on the demand for cookies – he knew that for the sake of variety, he needed to make at least 45 bags of each type of cookie. As he was planning his cookie composition, he also realized he was constrained by time in putting together the cookie bags. Circle cookies and Stars cookies took 1 minute per bag to finish; because Stars and Stripes had more icing, it took 2 minutes to finish each bag. He allocated 420 minutes (7 hours) to put the bags together. Can you determine how many of each of the three cookie types your friend should make to maximize sales (a surrogate for profit)? To quote POTUS: “Yes, you can!”

•2nd paragraph – consider that there are 3 boxes and that you don’t have to fill up the boxes (but you cannot exceed that space).

Each bag of Stars takes up 0.01 (1/100th) of a box

Each bag of Circles takes up 0.008 (1/125th) of a box

Each bag of Stars/Stripes takes up 0.0125 (1/80th) of a box

Use this information to help you in creating the LP Model.

I changed these specs to help simplify the input.

Can you provide a screenshot of how you would set this up in solver?

Answer 1

The optimal sales is equal to $ 348.75

The optimal number of bags of each type of cookie will be

x = 135
y = 45
z = 120