Problem $3.$ Sensitivity questions $30$ points

A small company that produces craftsmanship clocks. Two of the employees, Perla and Rebeca

can work upto $40$ hours a week, but the third employee, Jack, can only work $20$ hours per week.

The company makes two types of clocks: Grandfather Clock and Wall Clock, and ships to the

Also, in order to get the special discount from the trucking company Jack agrees to ship at least $7$ products weekly.

If each Grandfather $($G$)$ Clock brings a profit of $$300$ and each Wall $($W$)$ Clock generates a profit of $$200,$ what

would be the best product mix to optimize the firm's weekly profit, given that there is enough demand.

ABC Consulting runs an LP model for the company's weekly production plans using the model in the next worksheet

and generates the results provided in the Q$3$ Answer Report and Q$3$ Sensitivity Report $.$ Using these worksheets answer the following questions.

You can input the above symbolic model into the excel worksheet and solve using SOLVER; which is $20$ points. But to answer the following

sensitivity questions, the model is already solved and the Answer and Sensitivity

Reports are generated. See these reports in the corresponding worksheets and

answer the following questions $[$Of course give reasons for gour answers$]$:

Note that, neither of the owners understands this technical jargon. Therefore write your answers

a$)$ What is the optimum weekly product mix to be manufactured by the company? Write in terms of the product names

b$)$ Does any of the employe$($s$)$ has free time left during a week to due to this optimum production plan in part a$?$

If so$,$ who is that person and how many hours does they have idle?

c$)$ If the trucking company force the company to ship at least $8$ product per week, does it change their production mix given all other parameters the same? And what is the impact on the profit?

d$)$ For the following market changes, i$.$e$.,$ price changes for clocks:

d$1.$ If the retailers decides to discount G Clock's price, so that PeReJa's profit margin has to be reduced to $$265\mathrm{.}99?$

d$2.$ If the market appreciates W Clock more and the profit margin increase up to $$224\mathrm{.}99?$

Does the company has to change the weekly production mix, i$.$e$.,$ number of products to produce?

Not that you are asked to claim if a change has to be done or not, not the amount of change!