National Business Machines manufactures x model A fax machines and y model B fax machines. Each model A costs $100 to make, and each model B costs $150. The profits are $45 for each model A and $40 for each model B fax machine. If the total number of fax machines demanded per month does not exceed 2500 and the company has earmarked no more than $600,000/month for manufacturing costs, how many units of each model should National make each month to maximize its monthly profit?(x, y) =     What is the optimal profit?$

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Asked Sep 27, 2019
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National Business Machines manufactures x model A fax machines and y model B fax machines. Each model A costs $100 to make, and each model B costs $150. The profits are $45 for each model A and $40 for each model B fax machine. If the total number of fax machines demanded per month does not exceed 2500 and the company has earmarked no more than $600,000/month for manufacturing costs, how many units of each model should National make each month to maximize its monthly profit?

(x, y)  = 
 


  
 



What is the optimal profit?
$  

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Expert Answer

Step 1

The total number of fax machines demanded per month does not exceed 2500.

So, x+y<=2500

Step 2

The company has earmarked no more than $600,000/month for manufacturing costs.

Total cost= 100x+150y

So, 100x+150y<= 600000

Step 3

Total monthly profit= 40x+45y

So we have to maximize P=40x+45y

Subject to: x+y&l...

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Maximize: P 40x+45y subject to X+y2500 100x+150y 600000 x>0 y0

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