A firm produces
n different goods using m different raw materials.
Let bi be the available amount of the ith raw material.
Let xj be the amount of the jth good.
The jth good requires aji units of the ith material and results in a revenue of cj per unit produced.
How much of each good should we produce to maximize total revenue.
We can formulate
this problem as the following LP:
objective function: c1*x1 + ... + cn*xn
constraints: a1i*x1 + ... + ani*xn <= bi i=1...m
xj >= 0 j=1...n
in some #s:
2 goods: tricycles (good 1), and space shuttles (good 2)
revenue for each: c1 = $1, c2 = $3
2 raw materials: ranch dressing (material 1), and cheezy poofs (material 2)
amount of each: b1 = 500 tons, b2 = 200 tons
the goods require the following amounts of raw materials:
tricycles: a11 = 4 ton, a12 = 1 ton
space shuttles: a21 = 5 tons, a21 = 0 tons
objective function: 1*x1 + 3*x2
constraints: x4 + 5x2 <= 500
x1 <= 200
Example 2: View Frustum Culling