Question #53066

The following linear programming model formulation is used for the production of four different products, with two different manufacturing processes and two different material requirements:

Maximize Z= 50x1 + 58x2 + 46x3 + 62x4

Subject to

4x1 + 3.5x2 + 4.6x3 + 3.9x4 ≤ 600hr. (process 1)

2.1x1 + 2.6x2 +3.5x3 + 1.9x4 ≤ 500 hr. (process 2)

15x1 + 23x2 + 18x3 + 25x4 ≤ 3,600 lb. (material A)

8x1 + 12.6x2 + 9.7x310.5x4 ≤ 1,700 lb. (material B)

X1+x2¬¬¬¬¬___ ≥ .60

X1+x2+x3+x4

X1,x2,x3,x4 ≥ 0

A) Solve this problem by using the computer

B) Identify the sensitivity ranges for the objective function coefficients and the constraint quantity values.

C) Which is the most valuable resource to the firm

Maximize Z= 50x1 + 58x2 + 46x3 + 62x4

Subject to

4x1 + 3.5x2 + 4.6x3 + 3.9x4 ≤ 600hr. (process 1)

2.1x1 + 2.6x2 +3.5x3 + 1.9x4 ≤ 500 hr. (process 2)

15x1 + 23x2 + 18x3 + 25x4 ≤ 3,600 lb. (material A)

8x1 + 12.6x2 + 9.7x310.5x4 ≤ 1,700 lb. (material B)

X1+x2¬¬¬¬¬___ ≥ .60

X1+x2+x3+x4

X1,x2,x3,x4 ≥ 0

A) Solve this problem by using the computer

B) Identify the sensitivity ranges for the objective function coefficients and the constraint quantity values.

C) Which is the most valuable resource to the firm

Expert's answer

A) We can solve this problem by using the computer in excel using solver, where we need to write our requirements.

B) The sensitivity ranges for the objective function coefficients and the constraint quantity values will be found after the solver finds the maximizing quantities.

C) The most valuable resource to the firm is material A.

B) The sensitivity ranges for the objective function coefficients and the constraint quantity values will be found after the solver finds the maximizing quantities.

C) The most valuable resource to the firm is material A.

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