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Your computer supply store sells two types of inkjet printers. The first, type A, costs $267 and you make a $24 profit on each one. The second, type B, costs $127 and you make a $20 profit on each one. You can order no more than 170 printers this month, and you need to make at least $3760 profit on them. If you must order at least one of each type of printer, how many of each type of printer should you order if you want to minimize your cost?

a)80 of type A
90 of type B
b)68 of type A
102 of type B
c)102 of type A
68 of type B
d) 90 of type A
80 of type B

Respuesta :

LilyLikesMusic
The answer will be A.
Equation: (80 times 24) plus (90 times 20)

Answer:

d) 90 of type A

80 of type B

Step-by-step explanation:

The two equations form :  

[tex]a+b\leq 170[/tex]  ---- (1)

[tex]24a+20b \geq 3760[/tex]   ------(2)

Lets solve the first equation for either a or b;

[tex]b= 170-a[/tex]

Plug this into the second equation for b;

[tex]24a+20(170-a) \geq 3760[/tex]

=> [tex]24a+3400-20a \geq 3760[/tex]

=> [tex]4a+3400 \geq 3760[/tex]

=> [tex]4a \geq 3760-3400[/tex]

=> [tex]4a \geq 360[/tex]

=> [tex]a \geq 90[/tex]

Plugging in equation (1) to get value of b.

[tex]90+b\leq 170[/tex]

=> [tex]b\leq 80[/tex]

The answer is : d) 90 of type A

80 of type B

Note: if we choose 102 of type A and 68 of type B it will cost more. But choosing 90 of type A and 80 of type B will minimize the cost.

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