# Linear Programming 3 decision variables (past exam paper question)

This is an exam question I was practising. I have the general understanding of Linear programming, but how would you go about finding the Decision Variables, Objective function and Constraints for this?

My Opinions: Decision variables: $M_1$- # of Model $1$ to be produced $M_2$ and $M_3$(similar definition as $M_1$)

Objective function: I'd Multiple the Cost to make in house by cost to buy from subtractor

to get Minimise: $3900M_1+7500M_2+27300M_3$

Constraints: $3M_1+1.5M_2+2M_3\ge0$

$1.25M_1+2.5M_2+0.75M_3\ge8500$

$M_1,M_2,M_3\ge 5500$

No idea where number order would go? Do I use it in the Constraints and multiply by the Hours?

Now, am I on the right track?

You have to make a make-or-buy decision.

Let $M_i$ the amount of inhouse produced metal rings i.

And $B_i$ the amount of metal rings i, which is produced by the subcontractor.

The first two constraints are, that the inhouse production is limited due to availability of binding hours and harnessing hours.

$3M_1+1.5M_2+2M_3\leq 8,500$

$1.25M_1+2.5M_2+0.75M_3\leq 5,500$

The sum of inhouse product i and subcontractor produkt i has to be equal to the ordered amount of product i

$M_1+B_1=3450$

$M_2+B_2=1900$

$M_3+B_3=1100$

variables:

$M_1 ,M_2 ,M_3 ,B_1, B_2, B_3 \geq 0$

The objective function is the cost function. This is the sum of amounts of products ($M_i,B_i$) multiplied by their unit costs. How does it look like ?

• So would the object function look like this? Minimise : 60M1+75M2+210M3+65B1+100B2+130B3 – Mi-lee Wilson May 5 '15 at 17:05
• @Mi-leeWilson Like what ? – callculus May 5 '15 at 17:06
• I edited and thank you so much I have the exam in less than 1 hr. – Mi-lee Wilson May 5 '15 at 17:10
• @Mi-leeWilson You mean the edit 55 min ago ? No, this is not the right obj. function. You have given the values of the unit costs. This values must be in the obj. function. – callculus May 5 '15 at 17:14
• Those are the only cost given that is in the table. Cost in house and by sub-tractor are given in the table and are different. – Mi-lee Wilson May 5 '15 at 17:18