Use the Following Management Scientist Output to Answer the Questions $3 X 1 + 5 X 2 + 2 X 3 > 90$

question 2

Essay

Use the following Management Scientist output to answer the questions.
LINEAR PROGRAMMING PROBLEM
MAX 31X1+35X2+32X3
S.T.
OPTIMAL SOLUTION
Objective Function Value = 763.333
1) $3 X 1 + 5 X 2 + 2 X 3 > 90$
2) $6 \mathrm { X } 1 + 7 \mathrm { X } 2 + 8 \mathrm { X } 3 < 150$
3) $5 \mathrm { X } 1 + 3 \mathrm { X } 2 + 3 \mathrm { X } 3 < 120$ $$\begin{array} { l c c } \text { Variable } & \text { Value } & \text { Reduced Cost } \\\mathrm { X } 1 & 13.333 & 0.000 \\\mathrm { X } 2 & 10.000 & 0.000 \\\mathrm { X } 3 & 0.000 & 10.889\end{array}$$ OBJECTIVE COEFFICIENT RANGES
$$\begin{array} { l c c } \text { Constraint } & \text { Slack/Surplus } & \text { Dual Price } \\1 & 0.000 & - 0.778 \\2 & 0.000 & 5.556 \\3 & 23.333 & 0.000\end{array}$$ RIGHT HAND SIDE RANGES
$$\begin{array} { l l l l } \text { Variable } & \text { Lower Limit } & \text { Current Value } & \text { Upper Limit } \\\text { X1 } & 30.000 & 31.000 & \text { No Upper Limit } \\\text { X2 } & \text { No Lower Limit } & 35.000 & 36.167 \\\text { X3 } & \text { No Lower Limit } & 32.000 & 42.889\end{array}$$ $$\begin{array} { l c c l } \text { Constraint } & \text { Lower Limit } & \text { Current Value } & \text { Upper Limit } \\1 & 77.647 & 90.000 & 107.143 \\2 & 126.000 & 150.000 & 163.125 \\3 & 96.667 & 120.000 & \text { No Upper Limit }\end{array}$$
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:

Indifference Map

A set of indifference curves, each representing a different level of utility, that together show the preferences of a consumer.

Budget Line

A graphical representation of all possible combinations of two goods that can be purchased with a given budget at fixed prices.

Money Income

The total amount of monetary earnings or inflow received by an individual or entity, typically measured within a certain time period.

Budget Line

A graphical depiction of all possible combinations of two goods that can be purchased with a fixed amount of income, given their prices.