Minus Mufflers provides three types of automobile service for their customers - (1) extraneous muffler replacements, (2) bogus radiator repairs, and (3) unnecessary brake-pad replacements. Three of Minus's employees do all the work. Mr. Henry is the only employee customers are allowed to talk to. Mr. Henry's job includes, greeting the customers, describeing what is wrong with their car, the total costs involved and handling the paper work. A second employee, A. Capone is the inspector. A. Capone is responsible for examining the cars when they arrive at Minus and finding something wrong with the car. The third employee, Max, does all the repair work. The time required by each employee for each repair and the maximum number of hours each employee is willing to work per week is given in the table below. Minus ads guarantee their mufflers for the lifetime of the car. Therefore to avoid having to replace a muffler for free, Minus never installs their own brand, but rather installs A-1 mufflers. Minus has a contract to receive up to 40 A-1 mufflers per week (thus a maximum on only 40 muffler repairs can be performed each week). In addition, A Capone believes that at least 30% of the repairs should be radiator repairs. For kickback purposes, Mr. Haney requires that no more than 50% of repairs involve brake pad replacements. Finally, Max is unwilling to spend more than half of his actual working time (not the Maximum number of hours worked) performing radiator repairs. Formulate the LP model to maximize weekly profit and determine how many repairs of each time should be conducted per week.

Mr. Haney A.Capone Max
Service Profit time/repair time/repair time/repair
Muffler $70 15 minutes 10 minutes 30 minutes
Radiator $180 30 minutes 15 minutes 60 minutes
Brakes $95 15 minutes 15 minutes 20 minutes

Max hours/week 35 hours 25 hours 65 hours