Max (Z) = 3 X + 5Y Constraints: 2X +3Y≤ 30 5X +4Y≤60 By Condition X, Y20
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- Verify that in the example to the right, the same result isobtained if the constraint x + y = 20 is used to eliminate x rather than y.The owner of the Consolidated Machine Shop has $10,000 available to purchase a lathe, a press, a grinder, or some combination thereof. The following 0–1 integer linear programming model has been developed to determine which of the three machines (lathe, x1, press, x2, or grinder, x3) should be purchased in order to maximize annual profit: Maximize Z = 1000x1 + 700x2 + 800x3 (profit, $) subject to: $5,000x1 + 6,000x2 + 4,000x3 ≤ 10,000 (cost, $) x1 , x2 , x3 = 0 or 1 1. Solve this model by using the computer.construct the initial simplex tableau for the linear programming as follows: minimize z = 4x1 + 2x2 x1- x2 ≤ 150 -x1+ x2 ≤ 150 x1 +x2 ≥ 100 x1 +x2 ≤ 350 x1 + x2 ≥ 200 x1,x2 ≥ 0
- Find the minimum value of z = 4x2 + y2 − xysubject to the constraint 4x + y = 8. z =Glenmont Corporation wants to select 1 project from a set of 4 possible projects. Which of these constraints ensures only 1 project is selected? X1 + X2 + X3 + X4 ≥ 0 X1 + X2 + X3 + X4 ≥ 1 X1 + X2 + X3 + X4 = 1 X1 + X2 + X3 + X4 ≤ 1Solve the following Integer Programming problem Maximize z = 2x1 + 3x2 subject to 5x1 + 7x2 \leq35 4x1 + 9x2 \leq36 x1, x2 \geq 0 and integer