Question

Wandering through Wal-Mart one night, you come across a delightful looking bag (the Hershey's Super Mix Assorted Candy 32.9 oz, 70 ct. ) of candy which included three of your favorites – Heath Bar, Kit-Kat and Reese’s. Upon ripping open the bag later, you were dismayed to find few pieces of your favorites and almost 50% of the bag consisting of Milk Duds (appropriately named methinks!). When drifting off into Glucose Stuporland later that night on the couch, you dreamt a potential ‘fix it’ task: Determine a better bag of candy, using some real parameters, and a hypothetical “Candy Value” (among others), representing the desirability of each candy type based on a national average of polled candy consumers

So, the average “Candy Value” per piece for the 5 different candy types: Heath Bar (16), Kit-Kat (17), Milk Duds (5), Reese’s (13), Rolo (11) Other parameters of interest per candy per piece: Sugar content (in grams): Heath Bar (8.7), Kit-Kat (7.85), Milk Duds (6.7), Reese’s (7.4), Rolo (11) Weight (also in grams): Heath Bar (14), Kit-Kat (6), Milk Duds (12), Reese’s (14), Rolo (18) Chewiness (measures on a 1-10 scale, with 10 being crown-pulling chewy and 1 being teeth-breaking hard):

Heath Bar (1), Kit-Kat (5), Milk Duds (10), Reese’s (6), Rolo (7)

Requirements for your bag of candy:

1) Between 68 and 75 pieces, inclusive.

2) One candy type cannot make up more than 32% of the total number of pieces.

3) One candy type cannot make up less than 10% of the total number of pieces.

4) Milk Duds are of course especially despised. Add an additional requirement that no more than 16 Milk Duds packages can be present in the bag.

5) The maximum weight of all the candy combined cannot exceed 932 grams.

6) The average sugar content per piece of candy in the bag, to satisfy the Center for Science in the Public Interest, must not exceed 8.

7) The average chewiness in the bag, to satisfy the Center for Political Correct Dentistry, should be greater than or equal to 6.3.

8) Partial candies not allowed. Determine the optimal composition of the Super Mix bag that maximizes the total Candy Value of the bag using a LP model and the requirements provided above.

Answer 1