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Linear programming past 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?

Mi-lee Wilson
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1 Answers1

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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 ?

callculus42
  • 30,550
  • So would the object function look like this? Minimise : 60M1+75M2+210M3+65B1+100B2+130B3 – Mi-lee Wilson May 05 '15 at 17:05
  • @Mi-leeWilson Like what ? – callculus42 May 05 '15 at 17:06
  • I edited and thank you so much I have the exam in less than 1 hr. – Mi-lee Wilson May 05 '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. – callculus42 May 05 '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 05 '15 at 17:18
  • @Mi-leeWilson Sorry, you have edited your comment (I thought your question). I haven´t noticed it. YES, your objective function is RIGHT. BTW, good luck for your exam. – callculus42 May 05 '15 at 17:22
  • Thank you! One more thing since we are minimising objective function shouldn't 3M1+1.5M2+2M3>=8,500 1.25M1+2.5M2+0.75M3>=5,500 or is that only for material and not time. – Mi-lee Wilson May 05 '15 at 17:26
  • @Mi-leeWilson You have only 8500 and 5500 in the house. Thus the sums cannot not be greater than this numbers. The relations signs have to be $\leq$. It is comprehensible ? The objective function has nothing to do with the relation signs. – callculus42 May 05 '15 at 17:29
  • Thanks a lot this helped a lot. I Aced the test because of you. – Mi-lee Wilson May 05 '15 at 23:28
  • @Mi-leeWilson Nice to hear. Congratulation. Your are welcome. – callculus42 May 06 '15 at 04:11