Gatson manufacturing company produces 2 types of tires: Economy tire; Premium tire. The manufacturing time and the profit contribution per tire are given in the following table.
$$\begin{array} { | l | c | c | c | }
\hline { \text { Operation } } & \begin{array} { c }
\text { Manufacturing Time } \
\text { (Hours) }
\end{array} & { \text { Time Available } } \
\hline & \text { Economy tires } & \text { Premium tires } & \text { Hours } \
\hline \text { Material Preparation } & 4 / 3 & 1 / 2 & 600 \
\hline \text { Tire Building } & 4 / 5 & 1 & 650 \
\hline \text { Curing } & 1 / 2 & 2 / 4 & 580 \
\hline \text { Final Inspection } & 1 / 5 & 1 / 3 & 120 \
\hline \text { Profit/Tire } & \$ 12 & \$ 10 & \
\hline
\end{array}$$ Answer the following assuming that the company is interested in maximizing the total profit contribution.
a. What is the linear programming model for this problem?
b. Develop a spreadsheet model and find the optimal solution using Excel Solver. How many tires of each model should Gatson manufacture?
c. What is the total profit contribution Gatson can earn with the optimal production quantities?

Question

Gatson manufacturing company produces 2 types of tires: Economy tire; Premium tire. The manufacturing time and the profit contribution per tire are given in the following table.
​ $$\begin{array} { | l | c | c | c | } 
\hline  { \text { Operation } } & \begin{array} { c } 
\text { Manufacturing Time } \
\text { (Hours) }
\end{array} &  { \text { Time Available } } \
\hline  & \text { Economy tires } & \text { Premium tires } & \text { Hours } \
\hline \text { Material Preparation } & 4 / 3 & 1 / 2 & 600 \
\hline \text { Tire Building } & 4 / 5 & 1 & 650 \
\hline \text { Curing } & 1 / 2 & 2 / 4 & 580 \
\hline \text { Final Inspection } & 1 / 5 & 1 / 3 & 120 \
\hline \text { Profit/Tire } & \$ 12 & \$ 10 & \
\hline
\end{array}$$ Answer the following assuming that the company is interested in maximizing the total profit contribution. 
a. What is the linear programming model for this problem?
b. Develop a spreadsheet model and find the optimal solution using Excel Solver. How many tires of each model should Gatson manufacture?
c. What is the total profit contribution Gatson can earn with the optimal production quantities?

Quizplus · Accepted Answer

The Answer of Gatson manufacturing company produces 2 types of tires: Economy tire; Premium tire. The manufacturing time and the profit contribution per tire are given in the following table.
​ $$\begin{array} { | l | c | c | c | } 
\hline  { \text { Operation } } & \begin{array} { c } 
\text { Manufacturing Time } \
\text { (Hours) }
\end{array} &  { \text { Time Available } } \
\hline  & \text { Economy tires } & \text { Premium tires } & \text { Hours } \
\hline \text { Material Preparation } & 4 / 3 & 1 / 2 & 600 \
\hline \text { Tire Building } & 4 / 5 & 1 & 650 \
\hline \text { Curing } & 1 / 2 & 2 / 4 & 580 \
\hline \text { Final Inspection } & 1 / 5 & 1 / 3 & 120 \
\hline \text { Profit/Tire } & \$ 12 & \$ 10 & \
\hline
\end{array}$$ Answer the following assuming that the company is interested in maximizing the total profit contribution. 
a. What is the linear programming model for this problem?
b. Develop a spreadsheet model and find the optimal solution using Excel Solver. How many tires of each model should Gatson manufacture?
c. What is the total profit contribution Gatson can earn with the optimal production quantities?

Gatson Manufacturing Company Produces 2 Types of Tires: Economy Tire;