Problem I

Sklenka Ski Company $($SSC$)$ is a small manufacturer of two types of popular

all$-$terrain snow skis, the Jordanelle $($x$1)$ and the Deercrest $($x$2)$ models. The manufacturing process consists of two principal departments: fabrication and finishing. The fabrication department has $12$ skilled workers, each of whom works seven hours per day. The finishing department has three workers, who also work a seven$-$hour shift. Each pair of Jordanelle skis requires $3\mathrm{.}5$ labor hours in the fabricating department and $1$ labor$-$hour in finishing. The Deercrest model requires $4$labor$-$hours in fabricating and $1\mathrm{.}5$labor$-$hours in finishing. The company operates five days per week. SSC makes a net profit of $$50$ on the Jordanelle model and $$65$ on the Deercrest model. In anticipation of the next ski$-$sale season, SSC must plan its production of these two models. Because of

the popularity of its products and limited production capacity, its products are in high demand, and SSC can sell all it can produce each season. The company anticipates selling at least twice as many Deercrest models as Jordanelle models. The company wants to determine how many of each model should be produced on a daily basis to maximize net profit.

a$.$ Using Excel, Generate the answer and sensitivity reports.

b$.$What is the optimal solution?

c$.$ From the sensitivity report and without resolving the problem, answer

the following:

i$.$ Which resource would you like more of to earn more profit? How do

you know?

ii$.$ Which constraint$($s$)$ are non$-$binding?

iii. If the net profit for Jordanelle model was to increase from $$50$to $$60,$ how much additional net profit would be generated?

iv$.$ If the net profit for Deercrest model was to increase from $$65$to $$80,$ how much additional net profit would be generated?

v$.$ If the net profit for Deercrest model was to decrease from $$65$ to $$50,$ what would be the new maximum net profit?

vi $.$If you had the opportunity to hire two employees in the fabrication

department at an hourly wage of $$12\mathrm{.}50,$would you do so$?$ Explain

vii. If you had the opportunity to hire an employee in the finishing department at an hourly wage of $$50,$would you do so$?$ If yes, what would be the increase in net profit?

viii. If the machines in the fabrication department were down for

$2$ hours, what would be the impact?

$($It$\text{'}$s an assignment from chapter $3$ of the textbook "Introduction to Management Science, Global Edition Bernard W Taylor III $13$th edition"$)$