Once again i am stuck with this problem, i hope you help me out on this one.here is question
A produces three products from a raw material that in short supply.The Standard cos for raw material is $0.50 per kg.Detail of the products are also as follows;
product A product B product C
maximum sales demand 1000 2400 2800
production plan [units] 720 0 2800
contribution per unit $4.5 $4.8 $2.95
raw material per unit 2.5kg 3kg 1.5kg
A supplier has been found that is prepared to further supply 1000 kg of the material.
The maximum amount that the company should pay for the additional 1000 kg of the material is ?
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PMoptimum production
First we need to rank the products
0.
Product: A ***. B. ***. C
Contrib: $4.5 * $4.8 * $2.95
Mat/unit 2.5 * 3. *** 1.5
Cont/mat 1.8 * 1.2 * 1.97
Ranking. 2. * 3. ***. 1.
It looks like that the production plan is maximising the contribution.
1.
How many extra products we could produce and sell, if we buy the extra 1000kg raw material:
Product A demand less production plan:
1000 - 720 = 280
280 * 2.5kg = 440kg
660kg / 3 = 220 product B
2.
Calculate extra contribution.
280 * $ 4.5 = $ 1260
220 * $ 4.8 = $ 1056
Total: $ 3316
3. A
Max amount what the company could pay, if the fix costs are already absorbed:
Although the lower is the better
Material cost covered by the variable costs:
1000kg*0.5 = 500
Plus
Material cost covered by contribution:
3316
500 + 3316 = 3816
3. B
Max amount what the company could pay, if the fix costs haven't absorbed yet:
Although the lower is the better
Material cost covered by the variable costs:
1000kg*0.5 = 500
Plus
Material cost covered by contribution:
3316
500 + 3316 = 3816
Less outstanding part of fixed cost.
***
I am a student, my answer might be completely wrong...
i was thinking in line of shadow price but considering the 1000kg of the material.first u rank the products as contr/material, then u pick the one with highest contr then u add material price of $0.5/kg which gives u [$1.97 +$0.5] *1000kg.i dont if its ryt?
i was thinking in line of shadow price but considering the 1000kg of the material.first u rank the products as contr/material, then u pick the one with highest contr then u add material price of $0.5/kg which gives u [$1.97 +$0.5] *1000kg.i dont knw if its ryt?
It would be ok, but there is no more extra demand for product C.
That is why you have to calculate the shadow price with 280 A an 220. B
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