Cascade Inc. manufactures four different products for interior automotive protection: seat covers, all$-$weather floor mats, window sun shades, and cargo liners. Cascade Inc. earns a profit of $$100$ for each seat cover, $$75$ for each floor mat, $$75$ for a sun shade, and $$150$ for a cargo liner. A seat cover takes one hour of design time, two hours of manufacturing time, fifteen minutes of packaging time, and uses two kilowatt hours $($kWh$)$ of energy during production. A floor mat takes one hour of design time, one hour of manufacturing time, fifteen minutes of packaging time, and uses one kWh$.$ A sun shade takes two hours of design time, two hours of manufacturing time, ten minutes of packaging time, and uses one kWh$.$ A cargo liner takes three hours of design time, three hours of manufacturing time, twenty minutes of packaging time, and uses three kWh$.$ In a given month, you have $240$ hours of design time, $300$ hours of manufacturing time, $40$ hours of packaging time, and $350$ kWh$.$ Previous demand indicates that you need at least three times as many seat covers as sun shades and at least $50$ cargo liners.

Note: Please upload an Excel file and a Word file. The Excel file should contain three tabs: $(1)$ setup tab, $(2)$ answer report, and $(3)$ sensitivity report. The Word file should contain derivations and answers to the questions below.

$1.$ Use information in the Excel $$Answer Report$$ to answer the questions below.

a$.$ How many seat covers, floor mats, sun shades, and cargo liners should Cascade Inc. produce each month to maximize profit?

b$.$ How much profit does Cascade Inc. make per month?

c$.$ Which constraints are binding?

$2.$ Use information in the Excel $$Sensitivity Report$$ to answer the questions below.

a$.$ If the profit per floor mat decreased to $$60,$ how much profit would Cascade Inc. make?

b$.$ If the manufacturing time increased by $20$ hours, how much profit would Cascade Inc. make?

c$.$ If the profit per sun shade increased to $$135,$ would Cascade Inc. start producing sun shades?