Question
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
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: $19 each for the first 95 units, $18 each for units 96190, and $17 for each unit over 190. Product 2s profitability is $11 each for the first 70 units, $10 each for units 71140, and $9 each for each unit over 140. 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 | 3 | 7 | 1,000 |
B | 7 | 14 | 1,900 |
C | 14 | 14 | 1,800 |
Use separable programming to find the optimal production plan.
(Leave no cells blank be certain to enter "0" wherever required. Round the first two answers (units of Product 1 and 2) to the nearest whole number. Round the total profit answer to 2 decimal places and use unrounded unit quantities to compute it.)
______ Units of Product 1
______ Units of Product 2
______ The total profit from this plan will be
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