From the Regular$/$Premium gas example that we covered in class $($Example $15\mathrm{.}1$ in the book$)$:

a$)$ Use Simplex method to maximize the profits $"$by hand". You can use Excel if you want, but do every operation you would do by hand, and print every intermediate Simplex matrix

b$)$ Use the Excel Solver to maximize the profits. Which constraint$($s$)$ is limiting profit?

c$)$ To increase profits, the company wants to buy new equipment that can process gas more efficiently, so the plant will be able to process up to $90\frac{m^3}{?}$ week of raw gas and increase production time to $100h\frac{r}{w}$eek. Will you have enough storage for the new product amounts?

d$)$ The equipment vendor is selling the new equipment for $$25,000.$ If $80\%$ of the additional weekly profit obtained from the purchase of the equipment is used to make a weekly payment to the vendor, in how many weeks will you finish paying the new equipment? $($Assume that the vendor is not charging any interest and accepts weekly payments$)$