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: $12 each for the first 60 units, $11 each for units 61-120, and $10 for each unit over 120. Product 2's profitability is $18 each for the first 35 units, $17 each for units 36-70, and $16 each for each unit over 70. The products each require 3 raw materials to produce (see table below for usages and available quantities). Available Quantity Raw Material Product 1 usage (pounds Product 2 usage (pounds per unit) per unit) A 5 4 B с 7 11 11 11 (pounds) 1,600 1,200 2,000 Use separable programming to find the optimal production plan. (Leave no cells blank - be certain to enter "O" 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 and units of Product 2. The total profit from this plan will be

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter9: Decision Making Under Uncertainty
Section: Chapter Questions
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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: $12 each for the first
60 units, $11 each for units 61-120, and $10 for each unit over 120. Product 2's profitability is $18 each for the first 35 units, $17 each for
units 36-70, and $16 each for each unit over 70. The products each require 3 raw materials to produce (see table below for usages
and available quantities).
Available Quantity
Raw Material
Product 1 usage (pounds Product 2 usage (pounds
per unit)
per unit)
A
5
4
B
с
7
11
11
11
(pounds)
1,600
1,200
2,000
Use separable programming to find the optimal production plan.
(Leave no cells blank - be certain to enter "O" 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 and
units of Product 2.
The total profit from this plan will be
Transcribed Image Text: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: $12 each for the first 60 units, $11 each for units 61-120, and $10 for each unit over 120. Product 2's profitability is $18 each for the first 35 units, $17 each for units 36-70, and $16 each for each unit over 70. The products each require 3 raw materials to produce (see table below for usages and available quantities). Available Quantity Raw Material Product 1 usage (pounds Product 2 usage (pounds per unit) per unit) A 5 4 B с 7 11 11 11 (pounds) 1,600 1,200 2,000 Use separable programming to find the optimal production plan. (Leave no cells blank - be certain to enter "O" 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 and units of Product 2. The total profit from this plan will be
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