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

Question

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

Quizplus · Accepted Answer

The maximum profit possible is $125. This is determined by setting up the given linear programming model in Excel using Solver or a similar tool, inputting the constraints and objective function as given, and solving for the values of x1 (chairs) and x2 (tables) that maximize the profit equation, taking into account the setup costs and production constraints.

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

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