A fuel truck with 4 compartments needs to supply 3 different types of gas to a customer.
When demand is not filled, the company loses $0.25 per gallon that is not delivered.
How should the truck be loaded to minimize loss?
Truck Specifications
	Comp. 1	Comp. 2	Comp. 3	Comp. 4
Size (gallons)	1200	800	1300	700
Loading of Compartments (1=yes, 0=no)
	Comp. 1	Comp. 2	Comp. 3	Comp. 4
Gas 1	0	0	0	0
Gas 2	0	0	0	0
Gas 3	0	0	0	0
Total	0	0	0	0
Amount (gallons)
	Comp. 1	Comp. 2	Comp. 3	Comp. 4	Total	Demand	Loss
Gas 1	0	0	0	0	0	1800	$450.00
Gas 2	0	0	0	0	0	1500	$375.00
Gas 3	0	0	0	0	0	1000	$250.00
						Total Loss	$1,075.00
Maximum Amount (gallons)
	Comp. 1	Comp. 2	Comp. 3	Comp. 4
Gas 1	0	0	0	0
Gas 2	0	0	0	0
Gas 3	0	0	0	0
Problem
A fuel truck needs to supply 3 different kinds of gas to a customer. When demand is not filled the company
loses $0.25 per gallon that is not delivered. The truck has 4 separate compartments of different size. How
should the truck be loaded to minimize loss?
Solution
1) The variables are the decisions to fill the compartments for each type of gas, and the amounts to be put in
if the compartment is filled. In worksheet Knapsack, these are given the name Gallons_loaded and
Loading_decisions.
2) The logical constraints are
	Gallons_loaded >= 0 via the Assume Non-Negative option
	Loading_decisions = binary
Since there can only be one kind of gas in any compartment we have
	Total_decisions <= 1
The size limitations of the truck give
	Gallons_loaded <= Maximum_gallons
We don't want to load more than needed. This gives
	Total_gallons <= Demand
3) The objective is to minimize the loss. This is given the name Total_loss.
Remarks
It is often possible to have different objectives in these types of problems. We might, for instance, want to
minimize the wasted space in the truck in this example. Knapsack problems are characterized by a series of
0-1 integer variables with a single capacity constraint. If someone goes camping and his backpack can hold
only a certain amount of weight, what items should the camper bring? He should try to optimize the value
of the items while not exceeding the weight allowed by the backpack. There is a wide set of problems that
fall into this category.