Problem:
A chocolate maker has contracted to operate a small candy counter in a fashionable store. To start with, the selection of offerings will be intentionally limited. The counter will offer a regular mix of candy made up of equal parts of cashews, raisins, caramels, and chocolates, and a deluxe mix that is one-half cashews and one-half chocolates, which will be sold in one-pound boxes. In addition, the candy counter will offer individual one-pound boxes of cashews, raisins, caramels, and chocolates.
A major attraction of the candy counter is that all candies are made fresh at the counter. However, storage space for supplies and ingredients is limited. Bins are available that can hold the amounts shown in the following table:
Ingredient Capacity (Pounds/Day)
Cashews 120
Raisins 200
Caramels 100
Chocolates 160
In order to present a good image and to encourage purchases, the counter will make at least 20 boxes of each type of product each day. Assume that demand of the candies is such that regardless of candy mix all candy will be sold every day. Formulate the problem in order to maximize profit.
The profit per box for the various items is as follows:
Item Profit per Box
Regular $.80
Deluxe $.90
Cashews $.70
Raisins $.60
Caramels $.50
Chocolates $.75
Part A
Requirements:
1) Give a typed formulation with decision variables clearly defined and all constraints clearly defined.
2) Solve the formulation in solver and save the Sensitivity Report.
3) Using Sensitivity Analysis: If you had $6.00 to spend and it cost $1.50 to increase capacity of cashews by one pound, $1.20 to increase capacity of raisins by one pound, $0.60 to increase capacity of caramels by one pound, and $0.30 to increase capacity of chocolates by one pound; how would you spend the $6.00 to maximize your return and what would be your net return? Explain your answer.
4) Using Sensitivity Analysis: If the chocolate maker spends $10.00 on advertising for one of the products, he can then charge ten cents more per pound for this product and still be able to sell all he makes. Should he spend the $10.00 on advertising and if so how should he spend it to maximize net return?
Part B
The chocolate maker is considering broadening his candy selection by adding two candies to his selection: the regular candy with marshmallow topping and the deluxe candy with marshmallow topping. He will add 0.05 pounds of marshmallow topping on one pound of each of the regular or deluxe candies to make the new candies. Since he is not sure whether to add these candies he will not require a certain amount be made per day. He has space to add 10 pounds of marshmallow per day and the profit for the marshmallow regular is $1.00/pound and the marshmallow deluxe is $1.05/pound. Formulate the problem in order to maximize profit.
Requirements:
1) Give a typed formulation with decision variables clearly defined and all constraints clearly defined.
2) Solve the formulation in solver.