Reference no: EM133103317
Suppose that in a product mix problem, X1,X2,X3 and X4 indicate the units of products 1,2,3 and 4, respectively, and the LP Model Max 4x1, + 6x2 + 3x3 + 1x4Subject to:1.5X1 + 2X2 + 4X3 + 3X4 ≤ 550 Machine A hours4X1 + 1X2 + 2X3 +1X4 ≤ 700 Machine B hours2X1 + 3X2 + 2X4 ≤ 200 Machine C hoursX1, X2, X3, X4 ≥ 0
a. What is the optimal solution?
b. Which machines have excess capacity? How much?
c. If the objective function coefficient of X1, is increased by 0.50 will the optimal solution change?
d. Which constraints are binding?
e. Which constraints have surplus or slack?
f. If the current objective - function coefficient of X3 is decreased by 3, (assuming all the LP's other data remain unchanged) would the current optimal solution remain the same?
g. If one additional hour of Machine A is made available, how much would be the increase/improvement in the optimal solution?
h. Will an additional hour of Machine B improve the optimal solution? If yes, by how much?
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