I need a detailed explanation and assistance to solve this problem: FruitNuts is a store that sells a variety of unpackaged dried fruit and nut items. The current amounts of supplies of each item are listed in the following table: Item Supply (pounds) dried bananas 800 dried apricots 600 coconut pieces 500 raisins 700 walnuts 900 In addition to the individual items above, the store also sells two kinds of mix products: A Trail Mix product which consists of equal parts of all individual items above A Subway Mix product which consists of two parts walnuts and one part each of the dried bananas, raisins, and coconut pieces. To speed up service, the manager decides to package some of the merchandise in boxes ahead of time. Packaging and price data on boxes are shown below: Packaged Product Weight/Box (pounds) Price/Box ($) Trail Mix 2 7.00 Subway Mix 1 3.00 Dried Bananas 1 2.80 Dried Apricots 1 3.25 Coconut Pieces 1 3.60 Raisins 1 3.50 Walnuts 1 5.50 The manager decides that 50% of each of current supplies should be allocated for packaging in boxes, and the rest should be unpackaged. However, no more than 30% of the weight of packaged supplies should be allocated to mixes. Note that if any supplies allocated to packaging in boxes are not used in the optimal solution (that is, have slack), then the slack will be added to unpackaged supplies. FruitNuts wishes to use LP to determine the number of boxes for packaging products, so as to maximize the revenue from packaged product sales. - Write down the decision variables. - Write down the optimization statement for the objective function. - Write down the constraints.
I need a detailed explanation and assistance to solve this problem:
FruitNuts is a store that sells a variety of unpackaged dried fruit and nut items. The current amounts of supplies of each item are listed in the following table:
|
Item |
Supply (pounds) |
|
dried bananas |
800 |
|
dried apricots |
600 |
|
coconut pieces |
500 |
|
raisins |
700 |
|
walnuts |
900 |
In addition to the individual items above, the store also sells two kinds of mix products:
- A Trail Mix product which consists of equal parts of all individual items above
- A Subway Mix product which consists of two parts walnuts and one part each of the dried bananas, raisins, and coconut pieces.
To speed up
|
Packaged Product |
Weight/Box (pounds) |
Price/Box ($) |
|
Trail Mix |
2 |
7.00 |
|
Subway Mix |
1 |
3.00 |
|
Dried Bananas |
1 |
2.80 |
|
Dried Apricots |
1 |
3.25 |
|
Coconut Pieces |
1 |
3.60 |
|
Raisins |
1 |
3.50 |
|
Walnuts |
1 |
5.50 |
The manager decides that 50% of each of current supplies should be allocated for packaging in boxes, and the rest should be unpackaged. However, no more than 30% of the weight of packaged supplies should be allocated to mixes. Note that if any supplies allocated to packaging in boxes are not used in the optimal solution (that is, have slack), then the slack will be added to unpackaged supplies. FruitNuts wishes to use LP to determine the number of boxes for packaging products, so as to maximize the revenue from packaged product sales.
- Write down the decision variables.
- Write down the optimization statement for the objective function.
- Write down the constraints.
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