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: $13 each for the firs- 65 units, $12 each for units 66-130, and $11 for each unit over 130. Product 2's profitability is $17 each for the first 40 units, $16 each f units 41-80, and $15 each for each unit over 80. The products each require 3 raw materials to produce (see table below for usages and available quantities). Product 1 usage (pounds per unit) 5 Available Quantity (pounds) 2,300 1,700 1,100 Product 2 usage (pounds per unit) Raw Material 7 7 15 15 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.)

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Non-linear programming

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: $13 each for the first
65 units, $12 each for units 66–130, and $11 for each unit over 130. Product 2's profitability is $17 each for the first 40 units, $16 each for
units 41-80, and $15 each for each unit over 80. The products each require 3 raw materials to produce (see table below for usages
and available quantities).
Available Quantity
(pounds)
2,300
1,700
Product 1 usage (pounds
Product 2 usage (pounds
per unit)
Raw Material
per unit)
A
7.
15
15
1,100
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: $13 each for the first 65 units, $12 each for units 66–130, and $11 for each unit over 130. Product 2's profitability is $17 each for the first 40 units, $16 each for units 41-80, and $15 each for each unit over 80. The products each require 3 raw materials to produce (see table below for usages and available quantities). Available Quantity (pounds) 2,300 1,700 Product 1 usage (pounds Product 2 usage (pounds per unit) Raw Material per unit) A 7. 15 15 1,100 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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