A firm offers three different prices on its products, depending upon the quantity purchased. Since available resources are limited, the firm would like to prepare an optimal production plan to maximize profits. Product 1 has the following profitability: $10 each for the first 50 units, $9 each for units 51−100, and $8 for each unit over 100. Product 2’s profitability is $20 each for the first 25 units, $19 each for units 26−50, and $18 each for each unit over 50. The products each require 3 raw materials to produce (see table below for usages and available quantities). Raw Material Product 1 usage (pounds per unit) Product 2 usage (pounds per unit) Available Quantity (pounds) A 5 4 800 B 12 10 2,000 C 1,000 2,000 190,000 Use separable programming to find the optimal production plan. Note :Round all quantities to the nearest whole number and round profits to 2 decimal places. _______ units of Product 1 and _______ units of product 2. The total profit from this plan will be _______.
A firm offers three different prices on its products, depending upon the quantity purchased. Since available resources are limited, the firm would like to prepare an optimal production plan to maximize profits. Product 1 has the following profitability: $10 each for the first 50 units, $9 each for units 51−100, and $8 for each unit over 100. Product 2’s profitability is $20 each for the first 25 units, $19 each for units 26−50, and $18 each for each unit over 50. The products each require 3 raw materials to produce (see table below for usages and available quantities).
Raw Material | Product 1 usage (pounds per unit) | Product 2 usage (pounds per unit) | Available Quantity (pounds) |
---|---|---|---|
A | 5 | 4 | 800 |
B | 12 | 10 | 2,000 |
C | 1,000 | 2,000 | 190,000 |
Use separable programming to find the optimal production plan.
Note :Round all quantities to the nearest whole number and round profits to 2 decimal places.
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