Posted by fakaapo on Thursday, April 14, 2011 at 8:09am.
For the given linear prgramming problem, write down the objective function and the constraints.
Kris is trying to make his business more efficient by having a system of both large and small vans. He can spend no more than $100,000 for both type of vans and no more than $600 per month for maintenance. Kris can purchase a small van for $15,000 and maintain it for $100 per month. He can purchase a large van for $25,000 and maintain it for $70 per month. Each large van carries 14 passengers, and each small van carries 7 passengers. Kris is interested in knowing how many of each van he should purchase so that he can serve the maximum number of passengers.

math  MathMate, Thursday, April 14, 2011 at 10:18am
"large and small vans."
L=# of large, L≥0
S=# of small, S≥0
"He can spend no more than $100,000 for both type of vans"
"Kris can purchase a small van for $15,000 and maintain it for $100 per month...a large van for $25,000 and maintain it for $70 per month"
25000L+15000S≤100000
"no more than $600 per month for maintenance"
70L+100S≤600
"large van carries 14 passengers, and each small van carries 7 passengers"
Utility=objective function=
P(S,L)=7S+14L
So the above are the constraints and the objective function.
Note:
The formulation of the constraints and objective functions is a good exercise, especially when the parameters can change with time.
However, there are times that you don't need a screwdriver to do repairs. Same with linear programming:
Here:
Capacity of large van = 2*capacity of small
Cost of large van < 2*cost of small
cost of maintaining large van < 2*cost of maintaining small van
Number of large vans he can buy with budget=100000/25000 = exactly 4 (for 56 passengers)
cost of monthly maintenance = 4*70=280 < 600
So what would be your choice even without the screwdriver?