14 . a produced, He lauU more than one-third of the total number of units of pro

Question

14 . a

produced, He lauU more than one-third of the total number of units of product B should be 3 to 2: and there is a standing order for 5 units of product A each day. For- mulate a linear programming model for this problem, and then solve. 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 chocol 14. A chocolate maker has contracted to operate a small candy counter in a fashionable store. To start A major attraction of the candy counter is that all candies are made fresh at the counter. How- ever, storage space for supplies and ingredients is limited. Bins are available that can hold the amounts shown in the table: Capacity (pounds per day) 120 Ingredient Cashews Raisins Caramels 100 160 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. Any leftover boxes at the end of the day will be removed and given to a nearby nursing home for goodwill. The profit per box for the various items has been determined as follows: Item Regular Deluxe Cashews Raisins Caramels Chocolates Profit per Box $.80 90 .70 .60 .50 75 a. Formulate the LP model. b. Solve for the optimal values of the decision variables and the maximum profit.

Explanation / Answer

Solution

x1 = Regular mix

x2 = Deluxe mix

x3 = Cashews mix

x4 = Raisins mix

x5 = Caramels mix

x6 = Chocolates mix

The objective function is

Z = 0.8 x1 + 0.9 x2 + 0.7 x3 + 0.6 x4 + 0.5 x5 + 0.75 x6

The various constraints are

Regular mix has equal parts of cashews, raisins, caramels and chocolates.

So, reach pound of regular mix has 0.25 pounds of each cashews, raisins, caramels and chocolates.

Deluxe mix has equal parts of cashews, and chocolates.

So, reach pound of regular mix has 0.5 pounds of each cashews and chocolates.

So, the constraints in inequality form are

Cashews: 0.25x1 + 0.5 x2 + x3 120

Raisins: 0.25x1 + x4 200

Caramels: 0.25x1 + x5 100

Chocolates: 0.25x1 + 0.5 x2 + x6 160

Minimum boxes: x1, x2, x3, x4, x5, x6 20

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