Question

Sebastian owns a hobby shop. He sells model airplanes, trains, and cars. Sebastian earns $12 of profit per airplane, $10 of profit per train, and $8 of profit per car. He has 1,000 square feet of showroom space. Each airplane takes 4 square foot, each train takes 5 square feet, and each car takes 3 square feet. However, he doesn’t want the shop to look too clutter and therefore doesn’t want more than 300 total items on display. He also has 60 hours of time available to set up displays. It takes 12 minutes to set up an airplane, 20 minutes to set up a train and 10 minutes to set up a car. He expects to sell at least 20 cars and wants to have at least twice as many airplanes as trains.

If the profit per airplane increased by $2, what will be Sebastian’s profit?

Answer 1

To solve this, first we need to know the optimal number of airplanes, trains and cars.

Let x be the number of airplanes, y be the number of trains and z be the number of cars.

We need to maximise 12x+10y+8z subject to

Space-> 4x+5y+3z<=1000

Number->x+y+z<=300

Time->12x+20y+10z<=60*60=3600

z>20, x-2y>=0

solving them gives, x=235,y=0, z=20

By the time his profit increases, he would have set up his shop, so he wouldnt replace any stuff he already has. Hence, if profit per airplane increases by $2->235*14+20*8=3450