Problem: Stone Age Surfboards is a small manufacturer of two types of popular low$-$tide surfboards, the Graystone and the Lava models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has $8$ skilled workers, each of whom works $9\mathrm{.}25$ hours per day. The finishing department has $5$ workers, each of whom works a $6-$hour shift per day. Each pair of Graystone surfboards requires $2\mathrm{.}5$ labor hours in the fabrication department and $2$ labor hours in finishing. The Lava model requires $4\mathrm{.}2$ labor$-$hours in fabrication and $3\mathrm{.}6$ labor$-$hours in finishing. The company operates $6$ days a week. It makes a per$-$unit profit of $$40$ on the Graystone model and $$60$ on the Lava model. The company anticipates selling at least twice as many Lava models as Graystone models.

PART A: Create a mathematical model of the problem and solve it using Excel Solver. Upload the excel file $($name it: YourID#$.$xls$)$ on Moodle together with its sensitivity report. $($Assume fractional results are allowed$).(5$ pts$)$

PART B:Graphically solve the LP and verify that the solution matches with part A above. Upload a single picture file on Moodle $($name it: YourID#$.$jpeg$)($Total $5$ pts$)$

PART C: Answer each of the below questions with a relevant explanation. Upload a single word file on Moodle $($name it: YourID#$,$doc$).$ Make sure you indicate each answer corresponding to which question number. $($Total $5pts)$

What is the total number of hours used for fabrication and finishing operation?

What is the total profit generated?

What is the value of slack obtained from the answer report?

What is the Allowable Increase for Lava surfboards produced?

What is the Allowable Decrease for Graystone surfboards produced?

What is the shadow price for the finishing hours used?

What is the Allowable Increase in the finishing hours used?

What is the Allowable Decrease in the fabrication hours used?

What will be the total profit contribution from Lava surfboards?

What will be the total profit contribution from Graystone surfboards?