A chocolate maker has contracted to operate a small candy counter in a fashionable store. To startwith, the selection of offerings will be intentionally limited. The counter will offer a regular mixof candy made up of equal parts of cashews, raisins, caramels, and chocolates, and a deluxe mixthat 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, andchocolates.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 theamounts shown in the table.IngredientCapacity(pounds per day)Cashews 120Raisins 200Caramels 100Chocolates 160In order to present a good image and to encourage purchases, the counter will make at least 20boxes of each type of product each day. Any leftover boxes at the end of the day will be removedand given to a nearby nursing home for goodwill.The profit per box for the various items has been determined as follows.Item Profit per BoxRegular $.80Deluxe .90Cashews .70Raisins .60Caramels .50Chocolates .75a. Formulate the LP model.b. Solve for the optimal values of the decision variables and the maximum profit.

Practical Management Science
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ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
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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 table.
Ingredient
Capacity
(pounds per 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. 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 Profit per Box
Regular $.80
Deluxe .90
Cashews .70
Raisins .60
Caramels .50
Chocolates .75
a. Formulate the LP model.
b. Solve for the optimal values of the decision variables and the maximum profit.

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