solve using MS excel solver Jabba the Hutt, a greedy crime lord in the desert kingdom of Tatooine, has kept a group of

students from Earth, led by Tara, as captives while they were exploring Tatooine as a part

of a space tourism program. On learning that Tara is an expert in analytics, Jabba agrees

to release them in exchange of a weekly production plan that optimizes operations of their

company, Huttese Space Mobiles $($HSM$),$ that specializes in spaceships.

HSM manufactures two kinds of spaceships: a premium model built with hyperspace

technology called $$Space Falcon $($SF$)$ and a base model called $$Space Explorer $($SE$),$

which are sold at $700$ and $500$ Tatooine Dollars $($TD$),$ respectively. These spaceships are

usually assembled from parts supplied by space scavengers that come at a cost of $400$ TDs

for a unit of SF and $300$ TDs for a unit of SE$.$ While producing SF models is more

profitable, HSM cannot produce more than $40$ units of SF in a week because of an

agreement with a competing company, Bobba Space Mobiles $($BSM$).$

Given the harsh climate of Tatooine, manufacturing is constrained by water scarcity and

limited working hours. Moisture farming plants owned by HSM can collect at most $100$

gallons of water per week and moreover, with frequent sandstorms, HSM can only manage

up to $80$ assembly hours in a week. Producing a unit of SF requires $2$ gallons of water and

$1$ hr of assembly time whereas producing a unit of SE requires $1$ gallon of water and $1$ hr

of assembly time. Help Tara design a linear program to optimize weekly production in

HSM and answer Jabba$$s questions.

$($a$)$ Formulate the given problem as an LP$.$ Clearly define your decision variables, objective

function, and constraints.

$($b$)$ Draw a graphical representation of your LP$,$ clearly indicating the decision variables,

constraints, extreme points, feasible region, optimal solution, and optimum objective

function value.

$($c$)$ In the past few years, Bobba Space Mobiles $($BSM$),$ which produces $30$ units of SF per

week, has been more profitable than HSM$.$ Greedy Jabba thinks that producing more

than $30$ units of SF can help HSM overtake BSM$.$ Do you think this is a good idea?

Justify your answer.

$($d$)$ Jabba decides to increase the profits by making more water available for production.

What is the improvement in weekly profit that can be expected by providing an

additional gallon of water under the given conditions?

$($e$)$ Jabba$$s plan is to smuggle water from a nearby planet. However, space smuggling is

an extremely risky process. Jabba wants to know what is the maximum amount of water

that he should smuggle in order to improve the profits. Clearly show your calculations.

$($f$)$ Hearing about Jabba$$s plan to smuggle water, BSM makes a tricky offer to provide an

additional $60$ gallons of water at a fixed price of $3000$ TDs per week. Should Jabba

accept this offer? Explain your reasoning.

$($g$)$ Jabba wants to increase the selling price of spaceships by $100$ TDs but can only increase

the selling price of one of the models due to an agreement with BSM$.$ Jabba asks Tara

to analyze both scenarios. Which option do you think will be more profitable? What is

the maximum possible increase in weekly profits that can be expected? Show all your

workings.