You may produce seven products by consuming three materials. The unit sales price and material consumption of each product are listed in Table 1. For each day, the supply of these three materials are limited. The supply limits are listed in Table 2. For each day, you need to determine the production quantity for each product. Product Price Material 1 Material 2 Material 3 1 100 0 3 10 2 120 5 10 10 3 135 5 3 9 4 90 4 6 3 5 125 8 2 8 6 110 5 2 10 7 105 3 2 7 Table 1: Product information for Problem 1 Material Supply limit 1 100 2 150 3 200 Table 2: Material information for Problem 1 Formulate a linear integer program that generates a feasible production plan to maximize the total profit (which is also the total revenue, as there is no cost in this problem). Then write a computer program (e.g., using MS Excel solver) to solve this instance and obtain an optimal plan. Do not set the production quantities to be integer; leave them fractional. After you find an optimal solution and its objective value, write down the integer part of the objective value as your s
You may produce seven products by consuming three materials. The unit sales price and material consumption of each product are listed in Table 1. For each day, the supply of these three materials are limited. The supply limits are listed in Table 2. For each day, you need to determine the production quantity for each product.
Product |
Price |
Material 1 |
Material 2 |
Material 3 |
---|---|---|---|---|
1 |
100 |
0 |
3 |
10 |
2 |
120 |
5 |
10 |
10 |
3 |
135 |
5 |
3 |
9 |
4 |
90 |
4 |
6 |
3 |
5 |
125 |
8 |
2 |
8 |
6 |
110 |
5 |
2 |
10 |
7 |
105 |
3 |
2 |
7 |
Table 1: Product information for Problem 1
Material |
Supply limit |
---|---|
1 |
100 |
2 |
150 |
3 |
200 |
Table 2: Material information for Problem 1
Formulate a linear integer program that generates a feasible production plan to maximize the total profit (which is also the total revenue, as there is no cost in this problem). Then write a computer program (e.g., using MS Excel solver) to solve this instance and obtain an optimal plan. Do not set the production quantities to be integer; leave them fractional. After you find an optimal solution and its objective value, write down the integer part of the objective value as your solution (i.e., rounding down that value to the closest integer).
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