7-14 The Electrocomp Corporation manufactures two alectricall products : for conditionan and large for . The assembly process for each is solar in that both require a outan amount of wiring and drilling . Each air conditioner takes 3 howes of wiring and 3 hours of drilling . Each fon mount go through 2 hours of wiring and I hour of drilling . During the nast production period , 240 hours of wiring time are walable and up to 140 hours of drilling time maybe used . Each far conditioner cold yolds a profit of $23. Each fan assembled may be sold for a $15 profit . Formulate and solve this LF production mix Brunoion to find the but combination 8 of her conditioners and fans that ywe'ds the highest profit . Use the comer point graphical approach Lot X - the womber of air conditioners scheduled to be produced X. - the number of theis scheduled to be produced (maximize poofic ] 180 Subject to: IX. 140 (wiring capacity constraint ) 140 IX X. (drilling capacity comeraint ] Profit at point a (1=0 6-0) -50 Profit at point 6 (Y, - 0. V, = 120) - 25(0) . (15)(120) - 51,800 Profit at point e (1] - 40. N = 60) 25(40)+ (15x60) -31.900 Profit at point # (Y, -70. X -0) 25(70) + (15x0) -51.750 Optimal Solution : X, - 40 X - 60 Profit - $1,900 7-15 Electocorp's management realizes that it forgot to include two critical comerwants (saw Problem 7-14 ). In particular . management it dacides that to ansore an adequate supply of air conditioners for a contract , at least 20 air conditioners should be manufactured . Excause Electrocomp incurred an oversupply of theis in the proceding period management also insists that no more the 20 thes be produced during this production period . Resolve this product mix problem to find the now optimal solution Let X - the number of air conditioners scheduled to be produced X. - the womber of fans scheduled to be produced "maximize prost } (wiring capacity conscient ] 140 (drilling capacity contain ] (maximum # of fars corswain ) [non -angaunty commrains } Optimal Solution : X - 40 X: - 80 Profit - $1,900 7-16 A candidate for mayor in a small town has allocated $40,000 for fast -micone advertising in the daya proceding the alootion . Two types of ads will be wend : radio and television . Each radio ad cons $200 and reaches is estimated 2,000 people . Each television ad costs $500 and reaches an estimated 7,000 people . In planning the advertising campaign . the campaign manager would like to reach as many people as possible , but she has stipulaned that at least 10 ads of each cape mom be wed . Also , the number of radio ads moon be at least is grout is the number of television ads . How many ads of each cape should be wod 7 How many people will this reach X. - the womber of television ads purchased (maximize exposone 40.000 (budget constraint ] iv in X, LD (at least 10 radio ads porchand ) (at least WD television ads purchased ] (# of radio ads 2 = of television 24 ) (non -sagatity comming ) For solution purposes , the fourth consuming would be newroom Es X- X:2 0 Optimal Solution : X - 175 X - 10 Exposure - 195,000 people