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16 votes
16 votes
Maximize Z= 5X1 + 4X2

Subject to;
1.5X1 + 2.5X2 ≤ 80
2X1 + 1.5X2 ≤ 70
X1&X2 ≥ 0

User Musaffar Patel
by
2.9k points

1 Answer

17 votes
17 votes

Answer:

In this case, the optimal solution occurs at X1 = 40 and X2 = 0, which gives a maximum value of Z = 200. This means that if you produce 40 units of X1 and 0 units of X2, you will achieve the highest possible value of Z.

Explanation:

aX1 + bX2 ≤ c

where a, b, and c are constants.

The first constraint, 1.5X1 + 2.5X2 ≤ 80, is already in standard form. The second constraint, 2X1 + 1.5X2 ≤ 70, can be rewritten in standard form as follows:

-2X1 - 1.5X2 ≤ -70

You can now write the problem in the following standard form:

Maximize Z = 5X1 + 4X2

Subject to:

1.5X1 + 2.5X2 ≤ 80

-2X1 - 1.5X2 ≤ -70

X1, X2 ≥ 0

User Batfree
by
3.5k points
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