Question

Kevin is an auto mechan. He spends 3 hours when he replaces the shocks on a car and 2 hours when he replaces the brakes. He works no more than 48 hours a week. He routinely completes last 2 shocks replacements and brake replacements a week. If he charges $450 for labor replacing shocks and $250 in worfor replacing brakes, how many jobs of each type should be complete a week to maximize his income? Kevn should do shock replacements and trade replacements every week to maximize his weekly income

Answer 1

let us assume Kevin' does 'a' shock replacements and 'y' brake replacements. Then the constraints are : CŨ time < 48 – 320+ ay = 48 ( xsa, 976 We have to maximize income pe 4500C+ asoy let us sketch the feasible region: Shaded region s'our feasible region and min/max will occur at the (0,242 cogines points Corinen points are: (216), Cia,6), CQ,21) (0,6) Nowe we evaluate and the function - X=2 (2,21) 3x+2y = 48 (2,6) 4-6 (2/6) (200) (16,0) (14,4) Income C2,6) $2400 C1276) $6900 - Maximum C2,21) $6150 » Kevon should do ta shock replacements and brake replacements -