Consider the following linear program. Max 1A + 1B
s.t.
4A + 3B ≥ 24
2B ≥ 10
A, B ≥ 0
Does the linear program involve infeasibility, unbounded, and/or alternative optimal solutions? (Select all that apply.)
infeasibility
unbounded
alternative optimal solutions

Explain. (Select all that apply.)
The regions defined by the constraints do not overlap.
The first constraint allows the solution to be made infinitely large.
There are more than one solution for A and B which produce the optimal value for 1A + 1B.
The second constraint allows the solution to be made infinitely large.

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Ответ:

elleinad5656

23.09.2021

Mathematics

Only one solution $x=\frac{5}{4},y=0$

Step-by-step explanation:

$4x-5y=5..............(1)\\0.08x+0.10y=0.10...........(2)$

Multiply equation (2) by

4x-5y=5........(3)

Now from equation (1) equation (3)

$8x=10\\x=\frac{10}{8}\\x=\frac{5}{4}$

Put the value in equation (1)

$5-5y=5\\5y=0\\y=0$

hence only one solution exists $\left(\frac{5}{4},0\right)$ .

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