Use the Following Management Scientist Output to Answer the Questions

question 32

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 $$\begin{array} { c c c } \text { Variable } & \text { Value } & \text { Reduced Cost } \\\text { X1 } & 13.333 & 0.000 \\\text { X2 } & 10.000 & 0.000 \\\text { X3 } & 0.000 & 10.889\end{array}$$ $$\begin{array} { c c c } \text { Constraint } & \text { Slack/Surplus } & \text { Dual Price } \\1 & 0.000 & - 0.778 \\2 & 0.000 & 5.556 \\3 & 23.333 & 0.000\end{array}$$ OBJECTIVE COEFFICIENT RANGES $$\begin{array} { c c c c } \text { Variable } & \text { Lower Limit } & \text { Current Value } & \text { Upper Limit } \\\text { X1 } & 30.000 & 31.000 & \text { No Upper Limit } \\\text { X2 } & \text { No Lower Limit } & 35.000 & 36.167 \\\text { X3 } & \text { No Lower Limit } & 32.000 & 42.889\end{array}$$ RIGHT HAND SIDE RANGES $$\begin{array} { c c c c } \text { Constraint } & \text { Lower Limit } & \text { Current Value } & \text { Upper Limit } \\1 & 77.647 & 90.000 & 107.143 \\2 & 126.000 & 150.000 & 163.125 \\3 & 96.667 & 120.000 & \text { No Upper Limit }\end{array}$$
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:

Breakeven Point

is the level of production or sales at which total revenues equal total costs, resulting in neither profit nor loss.

Business Risk

Variation in a company’s financial performance caused by changes in business conditions.

Operating Leverage

A financial ratio that measures the degree to which a firm or project can increase operating income by increasing revenue, highlighting the impact of fixed costs on profits.

Fixed Costs

Expenses that do not change with the level of goods or services produced by a business over a certain period.