Solve the linear programming problem by the method of corners.
Minimize C = 4x + 3y
subject to x + y ≤ 48
x + 3y ≥ 60
9x + 5y ≤ 320
x ≥ 10, y ≥ 0
What is the minimum C? What is the point (X,Y)?

solve for y in the constraint equations.

you get:

x + y <= 48 becomes y <= (48 - x)

x + 3y >= 60 becomes y >= (60 - x)/3

9x + 5y <= 320 becomes y <= (320 - 9x) / 5

you also have the additional constraints of x >= 10 and y >= 0.

you will graph the equality portion of these constraints and then you will fill in the area that satisfies all the inequality portions of the constraints.

your graph will look like this:



the corner points of your feasible region are:

(10,38)
(20,28)
(10,16 and 2/3)
(30,10)

you evaluate your objective function of 4x + 3y at each of these corner points.

you will find that the minimum solution is at the point (10, 16 and 2/3) where the value of 4x + 3y is equal to 90.

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