Question

1. You own a franchise for delivering packages for several companies. You are going to buy a fleet of trucks and vans. You want to minimize the cost of the fleet while meeting all of the deliveries.

Type of Vehicle	Cost	Capacity (no. of deliveries/day)
Van	$30,000	200
Truck	$45,000	500

You have an average of 3000 deliveries per day. You must have at least one van.

Set up the integer programming problem.

Answer 1

X1 : Number of vans

X2 : Number of trucks

Number of deliveries per day for X1 vans

= Capacity for X1 vans = X1 x Capacity for one van = 200X1

Number of deliveries per day for X2Trucks

= Capacity for X2 trucks = X2 x Capacity for one truck = 500X2

Average deliveries to be made = 3000

200X1 + 500X2 3000

Cost of X1 vans = 30000X1

Cost of X2 trucks = 45000X2

Cost of the fleet : 30000X1 + 45000X2

You must have at least one van i.e X1 1

Minimize the cost the fleet : i.e

Minimize : 30000X1 + 45000X2

Subject to

200X1 + 500X2 3000

X1 1