A firm offers three different prices on its products, depending upon the quantity purchased. Since available resources are limited, thefirm would like to prepare an optimal production plan to maximize profits. Product 1 has the following profitability: $11 each for the first55 units, $10 each for units 56-110, and $9 for each unit over 110. Product 2's profitability is $19 each for the first 30 units, $18 each forunits 31-60, and $17 each for each unit over 60. The products each require 3 raw materials to produce (see table below for usagesand available quantities).Product 1 usage (poundsProduct 2 usage (poundsAvailable QuantityRaw Materialper unit)per unit)(pounds)A731,300BC141212151,5002,500Use 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 thenearest whole number. Round the total profit answer to 2 decimal places and use unrounded unit quantities to compute it.)units of Product 1 andunits of Product 2.The total profit from this plan will be

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College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.8: Linear Programming

Problem 5SC: If during the following year it is predicted that each comedy skit will generate 30 thousand and...

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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 an optimal production plan to maximize profits. Product 1 has the following profitability: $11 each for the first
55 units, $10 each for units 56-110, and $9 for each unit over 110. Product 2's profitability is $19 each for the first 30 units, $18 each for
units 31-60, and $17 each for each unit over 60. The products each require 3 raw materials to produce (see table below for usages
and available quantities).
Product 1 usage (pounds
Product 2 usage (pounds
Available Quantity
Raw Material
per unit)
per unit)
(pounds)
A
7
3
1,300
B
C
14
12
12
15
1,500
2,500
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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