Solve the Following Integer Linear Program

question 13

Short Answer

Solve the following integer linear program:

$\begin{array} { l l } \operatorname { MAX } & x _ { 1 } + x _ { 2 } \\\text { subject to: } & 4 x _ { 1 } + 6 x _ { 2 } \leq 22 \\& x _ { 1 } + 5 x _ { 2 } \leq 15 \\& 2 x _ { 1 } + x _ { 2 } \leq 9 \\& x _ { 1 } , x \geq 0 , \text { integer }\end{array}$

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Definitions:

Unit Contribution Margin

The amount each unit sold adds to profit, calculated by subtracting variable costs associated with a product from the sales price per unit.

Break-even Point

The juncture where total expenses match total income, resulting in neither a net profit nor a loss.

Fixed Expenses

Costs that do not change with the level of production or sales, remaining constant over a specified period.

Contribution Margin Ratio

A financial metric that measures the proportion of revenue remaining after variable costs have been deducted, indicating how much revenue is available to cover fixed costs and generate profit.