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I make model spaceships. Two kinds, the Ragnarok and the Sicarious. My Ragnarok takes 5 minutes to mold, 3 for the machining and 5 for the assembly. Each Sicarious takes 6 minutes for molding, 2 minutes to machine and 18 minutes of assembly. I can only afford to run my factory to accompany for 240 minutes of molding, 120 minutes of machining and 540 minutes of assembly time. I sell the Ragnarok for 45 dollars and the Sicarious for 20 dollars. How many of each should I produce to maximize profit? What is my profit?

Guest Oct 27, 2017
 #1
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Let  x be the number  of  Ragnarok and  y  the number of Sicarious

 

Here are the constraints :  

 

5x + 6y  ≤  240

3x  + 2y  ≤ 120

5x + 18y ≤  540

 

And we want to maximize this

45x +  20y

 

Look at the graph , here :

 

https://www.desmos.com/calculator/imsgkj9fb3

 

The profit will be maximized at an integer corner point in the feasible region....there is only one at (18 , 25)

 

So......we should produce 18 of the  Ragnarok  model  and 25 of the Sicarious model

 

And the max profit is  $ 1310

 

EDITED  ANSWER CORRECTING AN EARLIER MISTAKE  !!!

 

 

cool cool cool

CPhill  Oct 27, 2017
edited by CPhill  Oct 27, 2017
 #2
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Thanks man, you're the best!

Guest Oct 27, 2017

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