# Linear Programming model to maximize daily profit

1. A chocolate store has contracted to operate a small candy counter in a fashionable store. To start with, the selection of offering will be intentionally limited. The counter will offer a regular mix candy that is equal parts of cashews, caramels, and chocolates, and a deluxe mix that is one-half cashews and one-half chocolates. These will be sold in one-pound boxes. In addition, the candy counter will offer individual two-pound boxes of cashews, raisins, caramels, and chocolates.

A major attraction of the candy counter is that all candies are made fresh right at the counter. However, there is limited storage space for supplies and ingredients.

The current daily capacity and the cost per pound of each ingredient type are:

Ingredient Capacity (Pounds) Cost per Pound

Cashews 350 $3.50

Raisins 550 1.60

Caramels 420 2.80

Chocolates 510 3.20

In order to present a good image and to encourage purchases, the counter will make at least 55 boxes of each type of product each day. Any leftover boxes at the end of the day will be removed and given to a nearby nursing home for goodwill. The counter has $4,250.00 to allocate to these four ingredients. In addition, the profit from the deluxe mix boxes must be at least 20 percent of the total profit.

The selling price per box for the various items has been determined to be as follows:

Item Price

Regular $5.75

Deluxe 7.80

Cashews 5.35

Raisins 3.25

Caramels 3.80

Chocolates 4.10

a. Formulate a linear programming model to maximize daily profit for this model. Define all your variables.

b. Use LINDO or WINQSB to solve this model. Interpret your computer printout.

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#### Solution Preview

Attaching the solution for problem 1 as requested by you. Problem is solved by using MS Excel. That excel file is also attached. If you need any clarifications please contact.

1. Suppose the candy store produces X1 boxes of regular mix, X2 boxes of deluxe mix, X3 boxes of cashews, X4 boxes of raisins X5 boxes of caramels and X6 boxes of chocolates. It is given that the regular and deluxe mixes are sold in one pound boxes and individual items are sold in two-pound boxes. Further, the selling prices of these products per box are also given. Based on these data the profit per box of the various products can be calculated as follows.

Item Regular Deluxe Cashews Raisins Caramels Chocolates

Cost per box $3.17 $3.35 $7.00 $3.20 $5.60 $6.40

Selling price per box $5.75 $7.80 $5.35 $3.25 $3.80 $4.10

Profit per box $2.58 $4.45 -$1.65 $0.05 -$1.80 -$2.30

The profit function to be maximized is:

Constraints:

Capacity of cashew:

Capacity ...

#### Solution Summary

Linear programming model to maximize daily profits.