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?
Best Answer
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 ?