Question

There are 200 shirts and 100 pairs of trousers from last season that a retailer wants to get rid of. They've come up with two options, A and B, and are putting them together. Offer A is a $30 set that includes a shirt and a pair of trousers. Offer B is a $50 set that includes three shirts and two pairs of trousers. A total of 20 of Offer A and 10 of Offer B packages must be sold in order for the business to make a profit. Is there a maximum number of packets they need to sell in order to maximize profit?

Answer 1

Objective function

$30x+50y$

Constraints

$x+y≤100$

$x+3y≤200$

$x≥20,y≥10$

Feasible solution

Possible values Money generated ($)

(20,10) 30(20)+50(10)=1100

(90,10) 30(90)+50(10)=3200

(50,50) 30(50)+50(50)=4000

(20,60) 30(20)+50(60)=3600

To maximize profit they should sell 50 shirts and 50 trousers.