SOLUTION: I am completely stumped with this one! Please help! A company makes three products, A, B, and C. There are 500 pounds of raw material available. Each unit of product A require

Question 33389: I am completely stumped with this one! Please help!
A company makes three products, A, B, and C. There are 500 pounds of raw material available. Each unit of product A requires 2 pounds of raw material, each unit of product B requires 2 pounds of raw material, and each unit of product C requires 3 pounds. The assembly line has 1,000 hours of operation available. Each unit of product A requires 4 hours, while each unit of products B and C requires 5 hours. The company realizes a profit of $500 for each unit of product A, $600 for each unit of product B, and $1,000 for each unit of product C. Formulate (but don't solve) a linear program to determine how many units of each of the three products the company should make to maximize profits.
Answer by mukhopadhyay(490) (Show Source): You can put this solution on YOUR website!
Total available raw materials = 500 lbs; ...... (1)
Total available Operation hours = 1,000 hrs..... (2)
Raw material, hour, and profit requirements for each product is as following:
A - 2 lbs requiring 4 hours to make $500 profit;...(3)
B - 2 lbs requiring 5 hours to make $600 profit;...(4)
C - 3 lbs requiring 5 hours to make $1,000 profit;..(5)
Let x units of A, y units of B, and z units of C are required based on above rules;
The linear programs are as below:
2x+2y+3y <= 500 (based on 1,3,4,5)
4x+5y+5z <= 1000 (based on 2,3,4,5)
x,y,z are all integers
Profit will maximize if the raw materials and operation hours are utilized at their maximum availability.
So, maximizing x,y,z from the above-mentioned linear programs would give the number of units of each product to be manufatured to achieve maximum profit
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