math
posted by fakaapo .
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.

"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?
Respond to this Question
Similar Questions

PLEASE HELP... ALGEBRA.... LINEAR PROGRAMMING
HELP ME WITH THESE 2 PROBLEMS PLEASE..... 1. Objective Quantity: C= 5x+4y Constraints: x < 2 x > 4 y > 1 y < 6 All of the signs have lines under them. 2. Objective Quantity: C= 6x + 2y Constraints: x > 0 x < 5 y … 
Objective functon
An objective function and a system of linear inequalities representing constraints are given. Graph the system of inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region. … 
acc math 2 high school
I need help finding constraints to put this on the graph. the objective function is c=16x+25y. Problem: Your club plans to raisse money by selling two sizes of fruit baskets. The plan is to buy small baskets for $10 and sell them for … 
math
An objective function and a system of linear inequalities representing constraints are given. Graph the system of inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region. … 
algebra
Find the minimum and maximum values of the objective function subject to the given constraints? 
math
Write down the objective function and the constraints for the given linear programming problem. A local herb shop is producing two natural perfumes: Gentle Roseand Rich Gardenia. The owner, who has equipment that can make up to 3000 … 
Math
Your computersupply store sells two types of inkjet printers. The first, type A, costs $237 and you make a $22 profit on each one. The second, type B, costs $122 and you make a $19 profit on each one. You can order no more than 120 … 
Math/Management
MeanBeats is a company that manufactures and sells electronic musical equipment. Their headphone product line consists of two products, Reverbia and Bscape. MeanBeats sells the headphones to retailers at $600 and $300 per pack for … 
algebra 2
Graph the system of constraints and find the value of x and y that maximize the objective function. Constraints {x >= 0 y >= 0 y <= 3 y <= x+5} Objective Function C=5x+3y a) 0,0 b) 2,3 c) 5,0 d) 0,3 I am a mom going crazy. … 
Algebra 2
1. By graphing the system of constraints, find the values of x and y that maximize the objective function. 2<=x<=6 1<=y<=5 x+y<=8 maximum for p=3x+2y A. (2,1) B. (6,2) C. (2,5) D. (3,5) 2. By graphing the system of constraints, …