# math

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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 -

"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?