*Suppose that the finishing constraint now has 19 instead of 18 labor hours limi

Question

*Suppose that the finishing constraint now has 19 instead of 18 labor hours limit. Write the new finishing constraint.*

(Utilize info below)

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Maximize 80x +70y Subject to 6x + 3y <= 96 carpentry x + y <= 18 finishing constraints on labor hours in each manufacturing stage. 2x + 6y <= 72 upholstery x >=0, y >= 0 Study the solution of this problem below .This is called base case. The graph of the feasible set is made here for the formulated linear programming problem above 6x + 3y <= 96 x + y <= 18 2x + 6y <= 72 y >= 0 x y <= 32 - 2x y <= 18 - x y <= 12 - 1/3x y >= 0 0 32 18 12 0 2 28 16 11.33333333 0 4 24 14 10.66666667 0 6 20 12 10 0 8 16 10 9.333333333 0 10 12 8 8.666666667 0 12 8 6 8 0 14 4 4 7.333333333 0 16 0 2 6.666666667 0 18 -4 0 6 0 20 -8 -2 5.333333333

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Explanation / Answer

The new constraing would be: x + y <= 19.

0K. In first place, we have to take care that the sum of x and y does not exceed 18. so, we have to pick the appriopiate points from the table.

Looks like we can work with (0,12) , (16, 0), those values do not exceed the other constraints.

From the intersection of y <= 18 - x and y <= 12 - 1/3x, we get (9, 9).

From the intersection of y <= 32 - 2x and y <= 18 - x, we can also use (14 , 4).

So, we have to test those two points, and see which combination gives the maximum value.

For (0, 12): M = 80(0) + 70(12) = 840.

For (16, 0), M = 80(16) + 70(0) = 1280

For (9, 9) M = 80(9) + 70(9) = 1350

For (14, 4): M = 80(14) + 70(4) = 1400

So, the point (14, 4) is the one that gives the maximum value for the function.

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