7) Write ALL of the constraints and objective function required for this problem

Question

7) Write ALL of the constraints and objective function required for this problem. Do not attempt to solve.
A plant produces two kinds of products. Custom and Deluxe.
The profit for a Custom is $45 and a Deluxe $65. The plant can afford 1200 hours of machining. A custom takes 3 hrs and a deluxe takes 4.5 hours of machining. The plant can afford 500 hours of painting. A custom takes .5 hours of painting and a deluxe 1.5 hours of painting. The plant can afford 200 hours of packing. A custom takes .25 hours to pack and a deluxe takes .5 hours to pack.

Explanation / Answer

custom (x)                             deluxe (y)

$45                                       $65

3 hrs                                     4.5

.5 hrs                                    1.5

.25 hrs                                  .5

machining:   3x + 4.5y < 1200

painting:     0.5x + 1.5y < 500

packing:      0.25x + .5y < 200

then once these inequalities are solved, the x-value will be multiplied by $45, and the y-value will be multiplied by $65 for the total profit

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