Consider the Following Linear Programming Model and Risk Solver Platform

question 64

Essay

Consider the following linear programming model and Risk Solver Platform (RSP) sensitivity output. What is the optimal objective function value if the RHS of the first constraint increases to 18?
$$\begin{array} { l l } \operatorname { MAX } : & 7 \mathbf { X } _ { 1 } + 4 \mathbf { X } _ { \mathbf { 2 } } \\\text { Subject ta: } & 2 \mathbf { X } _ { 1 } + \mathbf { X } _ { \mathbf { 2 } } \leq 10 \\& \mathbf { X } _ { 1 } + \mathbf { X } _ { \mathbf { 2 } } \leq 10 \\& 2 \mathbf { X } _ { 1 } + 5 \mathbf { X } _ { \mathbf { 2 } } \leq 40 \\& \mathbf { X } _ { 1 } \mathbf { X } _ { \mathbf { 2 } } \geq \mathbf { 0 }\\\end{array}$$ $\text {Changing Calls}$
$\begin{array}{llrrrrr}&&\text { Final} &\text {Reduced }&\text {Objective }&\text {Allowable}&\text { Allowable }\\\text { Cell } & \text { Name } & \text { Value } & \text { Cost } & \text { Coefficient } & \text { Increase } & \text { Decrease } \\\hline \$ \mathrm{~B} \$ 4 & \text { Number to make: } \mathrm{X} 1 &6& 0 & 7& 1& 3\\\$ \mathrm{C} \$ 4 & \text { Number to make: } \mathrm{X} 2 & 4 & 0 &4 &3 & 0.5\\\end{array}$

$\text {Constraints}$
$\begin{array}{llrrrrr}&&\text { Final } &\text {Shadow} &\text { Constraint } &\text {Allowable} &\text { Allowable }\\\text { Cell } & \text { Name } & \text { Value } & \text { Price } & \text { R.H. Side } & \text { Increase } & \text { Decrease } \\\hline \$ \mathrm{D} \$ 8 & \text { Used } & 16&3 & 16&4&2.67 \\\$ \mathrm{D} \$ 9 & \text { Used } & 10 & 1&10 & 1 & 2 \\\$ \mathrm{D} \$ 10 & \text { Used } & 32& 0 & 40 & 1 E+30 & 8\end{array}$

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Definitions:

Barriers to Entry

Factors that prevent or hinder companies from entering a particular market or industry, such as high startup costs or complex regulations.

Consumer Ignorance

A situation where consumers lack necessary information about products or services, which can affect their buying decisions and market outcomes.

Inelastic Demand

A situation where the demand for a product does not significantly change in response to changes in its price.

Product Differentiation

The process of distinguishing a product or service from others, to make it more attractive to a particular target market involves variations in quality, features, or design.