Linear Programming Exercises

Please help me out with these three problems. Please note that these problems need to be completed manually.

7-14 The Electrocomp Corporation manufactures two electrical products: air conditioners and large fans. The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes 3 hours of wiring and 2 hours of drilling. Each fan must go through 2 hours of wiring and 1 hour of drilling. During the next production period, 240 hours of wiring time are available and up to 140 hours of drilling time may be used. Each air conditioner sold yields a profit of $25. Each fan assembled may be sold for a $15 profit. Formulate and solve this production-mix situation to find the best combination of air conditioners and fans that yields the highest profit. Use the corner point graphical approach.

7-15 Electrocomp's management realizes that it forgot to include two critical constraints (see Problem 7-14). In particular, management decides that there should be a minimum number of air conditioners produced in order to fulfill a contract. Also, due to an oversupply of fans in the preceding period, a limit should be placed on the total number of fans produced.
(a) If Electrocomp decides that at least 20 air conditioners should be produced, but no more than 80 fans should be produced, what would be the optimal
solution? How much slack is there for each of the four constraints?
(b) If Electrocomp decides that at least 30 air conditioners should be produced, but no more than 50 fans should be produced, what would be
the optimal solution? How much slack is there for each of the four constraints at the optimal solution?

7-18 The dean of the Western College of Business must plan the school's course offerings for the fall semester. Student demands make it necessary to offer at least 30 undergraduate and 20 graduate courses in the term. Faculty contracts also dictate that at least 60 courses be offered in total. Each undergraduate course taught costs the college an average of $2,500 in faculty wages, and each graduate course costs $3,000. How many undergraduate and graduate courses should be taught in the fall so that total faculty salaries are kept to a minimum?

Thank you for your help!