SOLUTION: 8) A small company makes masks and gloves. Resources required are cloth and labour. The company has 350 square cm of cloth and 50 hours of labour available. Each mask requires 20 s

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Question 1155592: 8) A small company makes masks and gloves. Resources required are cloth and labour. The company has 350 square cm of cloth and 50 hours of labour available. Each mask requires 20 square cm of cloth and 2 hours of labour, whereas each glove requires 60 square cm of cloth and 4 hours of labour. The profit for a mask is $5, and the profit for a glove is $10. The company wants to determine the number of masks and gloves to make so that profit will be maximized. Formulate a linear programming model for this problem.
Answer by ikleyn(52784)   (Show Source): You can put this solution on YOUR website!
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8) A small company makes masks and gloves. Resources required are cloth and labour.
The company has 350 square cm of cloth and 50 hours of labour available.
Each mask requires 20 square cm of cloth and 2 hours of labour, whereas
each glove requires 60 square cm of cloth and 4 hours of labour.
The profit for a mask is $5, and the profit for a glove is $10.
The company wants to determine the number of masks and gloves to make so that profit will be maximized.
Formulate a linear programming model for this problem.
~~~~~~~~~~~~~~~~~~ 

Let x be the number of masks and y be the number of gloves.


The objective function to maximize is the profit  P(x,y) = 5x + 10y  dollars.


The constraints are


20x + 60y <= 350  square cm of cloths;

 2x +  4y <= 50   hours;


x >= 0,  y >= 0.

The setups is just completed.

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To see many problems solved by the Linear Programming method,  look into the lesson
    - Solving minimax problems by the Linear Programming method
in this site.

Also,  look into the solutions of other similar problems in the archive to this forum under the links

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