Case Study $2$

Case Study: Bookstore $-$ Book Production Optimization

A bookstore publishes two types of books: Novels and Textbooks. Each Novel requires $4$ hours of writing and $2$

hours of editing, while each Textbook needs $3$ hours of writing and $4$ hours of editing. In the current schedule,

there are $40$ hours available for writing and $30$ hours available for editing. Each Novel sold yields a profit of

$$60,$ and each Textbook sold brings a profit of $$80$

Question:

Determine the optimal quantities of Novels $($x$)$ and Textbooks $($y$)$ to produce in order to maximize total profit,

considering the constraints on available hours for writing and editing in the bookstore's schedule.

Instructions:

Create the table

Complete algebraically

a$)$ Define the decision variables.

b$)$ Formulate the objective function.

c$)$ Set up the constraints.

Using Excel for QM$,$ solve the following linear programming problem for bookstore

Solve Graphically $-$ Use Solver

a$)$ Use the Corner$-$Point method $-$highlighting the corner points on the graph

i$)$ Solve equation $1$ and plot points for $x$ and $y$ on the graph

ii$)$ Solve equation $2$ and plot points for $x$ and $y$ on the graph

iii$)$ Determine the corner points on your graph $-$ highlight the feasible region

b$)$ Determine the maximum profit

i$)$ Solve both equation $1$ and $2$ for the unknown corner points for $x$ and $y$

ii$)$ Substitute all values from the corner points of $x$ and $y$ from the graph into the equation for

Maximum Profit and determine which combination of $x$ and $y$ will result in the Maximum

Profit

What would be your recommendations for bookstore?