could you please solve this as written exam and step by step with all the tables

1. ( 30 pts.) A company that manufactures three products, A,B, and C, using three machines, M1, M2, and M3, wants to determine the optimal production schedule that maximizes the total profit. Product A has to be processed by machines M1, M2, and M3, product B requires M1 and M3, while product C requires M1 and M2. The unit profits on the three products are $4,$2, and $5, respectively. The following linear program is formulated to determine the optimal product mix: Maviniar Z=4r4+2r1+5r3 eprimal valent Arvimum profit Z1390 shabow proce: 10,20, and 0 e for comtraints 1,2 and 3 repectively roduced coss for x1=30, for x1=0, for x1=0 HANGIS ON RICHE-HAND-SIDE (RIS) CONSIRARNTS RANGES ON OBSECTIVE FUNCTION COEFFCIFNTS Using the ahowe infonuation anwer the following questices a. Bccase of an increase in the cost of raw multrial uad for prodet C, its unit profit drops to 34. Deten ine the ncw optimal solesion and tle maximum peofit. b. Suppose it is possible to increase the capacity of coe of the machines. Which coe would you reoommend for expaniice and why? c. Due to an improvement in prodixt desige, the uait profil on product A can be iacreased to $6. Is is worthe hille producing product A now? Explain. d. Suppose thur tho eapscity of machine 2 can be increasod by another 200 minutes at a cost of 5250 . In it bconcemical to do sol Explain. e. Becmase of an iacrease in the cost of enensy for oporating the machines, the unit peofits of A. B. and C decrrae by $20,30.3, ana \$T. 2 , respectively. How with ir affect the epaimal wolutien and manimum profit