Problem $1(40$ pts$)$

Your friend is interning at a jewelry manufacfuring plant, in which two types of anklets

are produced. Anklet $1$ is composed of $2$ emerald gems and $3$ opal gems and requires $1$

hour of skilled labor. Anklet $2$ is composed of $3$ emerald gems and $2$ opal gems and

requires $2$ hours of skilled labor. Assume the demand for both types of anklets has no

limit$.$ The jewelry plant makes a profit of $$400$ for each anklet $1$ sold and $$500$ for each

anklet $2$ sold.

Currently, there are $100$ emerald gems and $120$ opal gems in inventory at the jewelry

plant. The plant's capacity of skilled labor is $70$ hours and could buy extra emerald gems

at a local supplier for $$100$ per emerald gem. To satisfy union rules, the plant must

produce at least $20$ anklet $1$ s and $25$ anklet $2$ s $.$

a$)$ Formulate a linear program to determine how many of each anklet type should be

produced at each plant to maximize profit. Describe in words what each constraint

written in the LP represents. $(15$ pts $)$

b$)$ Solve the LP from part a using Excel Solver. Provide a screenshot of the solved LP$,$

as well as of the Excel Solver window $($pre$-$solved$).(5$ pts$)$

c$)$ A new local supplier of opal gems has opened and is selling each opal gem for $$10.$

Should the jewelry manufacturer purchase some opal gems to improve the optimal

solution found in part b$?$ Without re$-$solving the LP$,$ explain and show work $($including

screenshots of any reports used$).(10$ pts$)$

d$)$ How much would the jewelry manufacturer be willing to pay for one extra hour of

skilled labor? Without re$-$solving the LP$,$ explain and show work $($including screenshots

of any reports used$).(10$ pts$)$