- This topic has 3 replies, 2 voices, and was last updated 8 years ago by
.
- Posts
A linear programming model has been formulated for two products, X and Y. The objective
function is depicted by the formula C = 5X + 6Y, where C = contribution, X = the number of
product X to be produced and Y = the number of product Y to be produced.
Each unit of X uses 2 kg of material Z and each unit of Y uses 3 kg of material Z. The
standard cost of material Z is $2 per kg.
The shadow price for material Z has been worked out and found to be $2.80 per kg.
If an extra 20 kg of material Z becomes available at $2 per kg, what will the maximum
increase in contribution be?
A Increase of $96
B Increase of $56
C Increase of $16
D No changeHere B is correct. Why we don’t deduct material cost?
The shadow price is the most extra that they would be prepared to pay for one extra kg of Z (and is calculated by working out how much one extra kg of Z would increase the contribution by).
So, by definition, the extra contribution would be the shadow price of 2.80 per kg.
Also, it means that they would be prepared to pay up to an extra 2.80 per kg – so a total of 4.80 per kg – for Z.
I do stress all of the above in my free lectures on linear programming.
But previously I commented to the following example – Practice question Chapter 6 (there is only one question in it):
A company currently makes two products – X and Y.Both use material Z which is in limited supply and current production level sare using entire weekly supply. Product X and Y use 5 kg each, product Z costs $3 and shadow price $3.75my comment:
” increase in contribution 3. 75 and most to pay 6. 75?”
You didn’t confirm this. Or I didn’t get you right?I just need to be sure my understanding is correct.Sorry.
The most to pay is $6.75 (because the increased contribution is 3.75 if they could buy more at 3.00).
The more they actually have to pay, the less the extra contribution will end up being. (So if they did have to pay (say) $5 per kg to buy more, then the extra contribution they would earn would be 3.75 – (5 – 3) = $1.75 per kg.
- The topic ‘Shadow price’ is closed to new replies.