Any topic (writer’s choice)
1) Gabi makes silver bracelets, necklaces, and earrings. She has a maximum of 160 hours per month to put in her work. She has 2,050 grams of silver available. The profit, labor time, and grams of silver required to produce each product are given in the following table.
Product
Unit Profit ($)
Labor per Unit (hours)
Silver per Unit (grams)
Bracelet
60
1.00
15
Necklace
80
2.00
20
Earring
30
0.75
8
If demand for each product is unlimited, how can Gabi maximize her profit?
Build an LP model to represent this problem
Build an Excel representation of the LP model
2) HealthTech Foods managers are considering developing a new low-fat snack food. The new product will be a blend of two types of cereals, each of which has different fiber, fat and protein characteristics. The following table shows these nutrition characteristics for one ounce of each type of cereal.
Cereal A
Cereal B
Dietary Fiber (grams)
2
1.5
Fat (grams)
2
3
Protein (grams)
4
3
Note that each ounce of Cereal A provides 2 grams of dietary fiber, and each ounce of Cereal B provides 1.5 grams of dietary fiber. Thus, if HealthTech were to develop the new product formula using a mix consisting of 50% Cereal A and 50% Cereal B, 1 ounce of the snack food would contain 1.75 grams of dietary fiber. HealthTech nutrition requirements call for each ounce of the new snack to have at least 1.7 grams of dietary fiber, no more than 2.8 grams of fat and no more than 3.6 grams of protein.
The cost of Cereal A is $0.020 per ounce and the cost of Cereal B is $0.025 per ounce. HealthTech wants to determine how much of each cereal is needed to produce 1 ounce of the new food product at the lowest possible cost.
Identify the decision variables and the objective, develop the objective function and the constraint inequalities, (and equations, if any), and bring them all together to form the LP model for this problem
Build an Excel representation of the LP model
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