Maximize 20X1 + 25X2 + 10X3 + 15X4 Total Profit Subject to X1 + X2 + X3 + X4 > 150 At least a total of 150 units of all four products are needed X1 + 3X2 + 2X3 + 2X4 ≤ 400 Resource 1 2X1 + X2 + 2X3 + X4 ≤ 280 Resource 2 And X1, X2, X3, X4 ≥ 0 Where X1, X2, X3 and X4 represent the number of units of Product 1, Product 2, Product 3 and Product 4 to be manufactured. The Excel Solver output for this problem is given below. (a) Determine the optimal solution and the optimal value for this problem and interpret their meanings. (b) Determine the slack (or surplus) value for each constraint in this problem and interpret its meaning.
Maximize 20X1 + 25X2 + 10X3 + 15X4 Total Profit Subject to X1 + X2 + X3 + X4 > 150 At least a total of 150 units of all four products are needed X1 + 3X2 + 2X3 + 2X4 ≤ 400 Resource 1 2X1 + X2 + 2X3 + X4 ≤ 280 Resource 2 And X1, X2, X3, X4 ≥ 0 Where X1, X2, X3 and X4 represent the number of units of Product 1, Product 2, Product 3 and Product 4 to be manufactured. The Excel Solver output for this problem is given below. (a) Determine the optimal solution and the optimal value for this problem and interpret their meanings. (b) Determine the slack (or surplus) value for each constraint in this problem and interpret its meaning.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Maximize 20X1 + 25X2 + 10X3 + 15X4 Total Profit
Subject to X1 + X2 + X3 + X4 > 150 At least a total of 150 units of all four products are needed
X1 + 3X2 + 2X3 + 2X4 ≤ 400 Resource 1
2X1 + X2 + 2X3 + X4 ≤ 280 Resource 2
And X1, X2, X3, X4 ≥ 0
Where X1, X2, X3 and X4 represent the number of units of Product 1, Product 2, Product 3 and Product 4 to be manufactured.
The Excel Solver output for this problem is given below.
(a) Determine the optimal solution and the optimal value for this problem and interpret their meanings.
(b) Determine the slack (or surplus) value for each constraint in this problem and interpret its meaning.
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