Chapter 3.4, Problem 15E

PRODUCTION SCHEDULING Soundex produces two models of satellite radios. Model A requires $15\text{min}$ of work on Assembly Line I and $10\text{min}$ of work on Assembly Line II. Model B requires $10\text{min}$ of work on Assembly Line I and $12\text{min}$ of work on Assembly Line II. At most $25\text{hr}$ of assembly time on Line I and $22\text{hr}$ of assembly time on Line II are available each day. Soundex anticipates a profit of $\$12$ on model A and $\$10$ on model B. Because of previous overproduction, management decides to limit the production of model A satellite radios to no more than $80/\text{day}$.

a. To maximize Soundex's profit, how many satellite radios of each model should be produced each day?

b. Find the range of values that the contribution to the profit of a model A satellite radio can assume without changing the optimal solution.

c. Find the range of values that the resource associated with the time constraint on Assembly Line I can assume.

d. Find the shadow price for the resource associated with the time constraint on Assembly Line I.

e. Identify the binding and nonbinding constraints.