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:

Sales Exceeding Budget

This indicates a financial scenario where actual sales revenue surpasses the projected figures in the budget, often viewed positively as it suggests higher profitability.

Maintenance Department

A functional area within an organization responsible for the continuous upkeep and repair of equipment, buildings, and facilities to ensure smooth and efficient operations.

Manufacturing Company

A business that produces finished goods from raw materials through the use of labor and machinery in a systematic process.

Cost Center

A function or department within an organization that does not directly add to profit but still incurs costs, such as HR or customer service departments.