Note: This Problem Requires the Use of a Linear Programming $$y _ { i } = \left\{ \begin{array} { l } 1 , \text { if product } j \text { is produced } \\0 , \text { otherwise }\end{array} \right.$$

question 9

Multiple Choice

Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver.
A manufacturer has the capability to produce both chairs and tables. Both products use the same materials (wood, nails and paint) and both have a setup cost ($100 for chairs, $200 for tables) . The firm earns a profit of $20 per chair and $65 per table and can sell as many of each as it can produce. The daily supply of wood, nails and paint is limited. To manage the decision-making process, an analyst has formulated the following linear programming model:
Max 20x1 + 65x2 - 100y1 - 200y2
s.t. 5x1 + 10x2 ? 100 {Constraint 1}
20x1 + 50x2 ? 250 {Constraint 2}
1x1 + 1.5x2 ? 10 {Constraint 3}
My1 ? x1 {Constraint 4}
My2 ? x2 {Constraint 5} $$y _ { i } = \left\{ \begin{array} { l } 1 , \text { if product } j \text { is produced } \\0 , \text { otherwise }\end{array} \right.$$
Set up the problem in Excel and find the optimal solution. What is the maximum profit possible?

• A) $25
• B) $50
• C) $75
• D) $100
• E) $125

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Definitions:

Average Costs

The total cost of production divided by the quantity produced, indicating the cost per unit of output.

Fixed Costs

Expenses that do not vary with the level of production or sales, such as rent, salaries, and loan payments.

Marginal Productivity

Marginal productivity measures the change in output resulting from altering the level of a single input while holding other inputs constant.

Marginal Costs

The added financial burden of creating one more unit of a product or service.