Question 8 (1 point) The Acme Class Ring Company designs and ses two types of ri

Question

Question 8 (1 point) The Acme Class Ring Company designs and ses two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring, versus 2 man hours to make one SST ring How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $40 and on arn SST ring is $35? O A) 14 VIP and 10 SST O B) 12 VIP and 12 SST O c) 18 VIP and 6 SST O D) 16 VIP and 8 SST Save

Explanation / Answer

Question 8:

Let the number of VIP rings produced be X and number of SST rings produced be Y. Then we are given the constraints here as:

X + Y <= 24

3X + 2Y <= 60

Total profit = 40X + 35Y

Here, we first try to solve the contraints equation as:

X + Y = 24,
Multiplying the above equation by 2, we get:
2X + 2Y = 48

3X + 2Y = 60

Subtracting 2X + 2Y = 48 from 3X + 2Y = 60 , we get:

X = 60 - 48 = 12

Y = 24 - 12 = 12

Profit in this case is computed as: 40X + 35Y = 40*12 + 35*12 = 900

The other corner points used could be given as:

X = 0 and Y = 24. This also satisfies 24*2 = 48 man hours contraint

btu profit here would be 24*35 = 840 < 900, therefore this cant be used.

Y = 0 and X = 24, but 3*24 = 72 man hours is more than 60 man hours.

Therefore, for Y = 0, we use X = 60/3 = 20

Profit = 20*40 = 800 < 900

Therefore B) 12 VIP and 12 SST rings are to be produced to maximize the profit here.

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