The Sunrise Raisin Company makes three different products from raisins: natural raisins (Natural), lightly coated yogurt raisins (Light), and heavily coated yogurt raisins (Heavy). The company is barely able to keep up with the increasing demand for these products. However, increasing raw material prices and market competition are forcing the company to watch its margins to ensure it is operating in the most efficient manner possible. To meet marketing demands for the coming week, the company needs to produce no more than 500 pounds of the Natural product, between 50 and 600 pounds of the Light product, and no more than 400 pounds of the Heavy product. Each pound of the Natural, Light, and Heavy product contains, respectively, 100%, 80%, and 50% raisins with the remaining weight made up of yogurt coating. The company has 825 pounds of raisins and 420 pounds of yogurt available for use in the next week. The various products are made by using three different machines that coat the raisins in yogurt (if needed), post-process the raisins/yogurt raisins, and package the products. The following table summarizes the time required by each product on each machine. Each machine has 10 hours of time available in the coming week. Minutes Required per Pound Natural Light Heavy Coating 0 2 3 Post-processing 1.1 1.5 1.7 Packaging 1.8 1.25 1.6 The selling price and variable cost associated with each pound of product is summarized in the following table: Per Pound Revenue and Costs Natural Light Heavy Selling Price $5.00 $9.50 $12.50 Variable Cost $1.20 $6.00 $7.30 The company wants to know how many pounds of each product should it produce in order to maximize its profit. Formulate an LP model for this problem in a Word file Create a spreadsheet model for this problem, and solve it using Solver in an Excel file
The Sunrise Raisin Company makes three different products from raisins: natural raisins (Natural), lightly coated yogurt raisins (Light), and heavily coated yogurt raisins (Heavy). The company is barely able to keep up with the increasing demand for these products. However, increasing raw material prices and market competition are forcing the company to watch its margins to ensure it is operating in the most efficient manner possible. To meet marketing demands for the coming week, the company needs to produce no more than 500 pounds of the Natural product, between 50 and 600 pounds of the Light product, and no more than 400 pounds of the Heavy product. Each pound of the Natural, Light, and Heavy product contains, respectively, 100%, 80%, and 50% raisins with the remaining weight made up of yogurt coating. The company has 825 pounds of raisins and 420 pounds of yogurt available for use in the next week. The various products are made by using three different machines that coat the raisins in yogurt (if needed), post-process the raisins/yogurt raisins, and package the products. The following table summarizes the time required by each product on each machine. Each machine has 10 hours of time available in the coming week.
|
Minutes Required per Pound |
|||
|
|
Natural |
Light |
Heavy |
|
Coating |
0 |
2 |
3 |
|
Post-processing |
1.1 |
1.5 |
1.7 |
|
Packaging |
1.8 |
1.25 |
1.6 |
The selling price and variable cost associated with each pound of product is summarized in the following table:
|
Per Pound Revenue and Costs |
|||
|
|
Natural |
Light |
Heavy |
|
Selling Price |
$5.00 |
$9.50 |
$12.50 |
|
Variable Cost |
$1.20 |
$6.00 |
$7.30 |
The company wants to know how many pounds of each product should it produce in order to maximize its profit.
Formulate an LP model for this problem in a Word file
Create a spreadsheet model for this problem, and solve it using Solver in an Excel file
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