Use the Following Management Scientist Output to Answer the Questions

question 12

Essay

Use the following Management Scientist output to answer the questions.
LINEAR PROGRAMMING PROBLEM
MAX
31X1+35X2+32X3
S.T.
1) 3X1+5X2+2X3>90
2) 6X1+7X2+8X3<150
3) 5X1+3X2+3X3<120
OPTIMAL SOLUTION
Objective Function Value = 763.333 $$\begin{array} { c r c } \text { Variable } & \text { Value } & \text { Reduced Cost } \\\text { X1 } & 13.333 & 0.000 \\\text { X2 } & 10.000 & 0.000 \\\text { X3 } & 0.000 & 10.889\end{array}$$ $\begin{array} { c c c } \text { Constraint } & \text { Slack/Surplus } & \text { Dual Price } \\ 1 & 0.000 & - 0.778 \\ 2 & 0.000 & 5.556 \\ 3 & 23.333 & 0.000 \end{array}$
OBJECTIVE COEFFICIENT RANGES
$\begin{array}{cccc}\text { Variable }&\text { Lower Limit } & \text { Current Value } & \text { Upper Limit }\\\hline\text { X1 } & 30.000 & 31.000 & \text { No Upper Limit } \\\text { X2 } & \text { No Lower Limit } & 35.000 & 36.167 \\\text { X3 } & \text { No Lower Limit } & 32.000 & 42.889\end{array}$
$\text { RIGHT HAND SIDE RANGES }$
$\begin{array}{cccc}\text { Constraint }&\text { Lower Limit } & \text { Current Value } & \text { Upper Limit }\\\hline1 & 77.647 & 90.000 & 107.143 \\2 & 126.000 & 150.000 & 163.125 \\3 & 96.667 & 120.000 & \text { No Upper Limit }\end{array}$
a.Give the solution to the problem.
b.Which constraints are binding?
c.What would happen if the coefficient of x₁ increased by 3?
d.What would happen if the right-hand side of constraint 1 increased by 10?

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Definitions:

Pistil

The female reproductive organ of a flower; consists of either a single carpel or two or more fused carpels. See carpel.

Structure Labeled

In microscopy, the identification and tagging of specific cellular or molecular components with labels or markers for study.

Anther

The part of the stamen in flowers that produces microspores and, ultimately, pollen grains.

Endosperm

A nutritive tissue in seeds of most flowering plants, providing sustenance to the developing embryo.