Question

inisiana For policy on late submissions, refer to the course's syllabus. sldowolla oldswollA nenes woboda able H. she Sulev Sm Problem 1 (40 pt) 00 2 레 OOS 2Hgnitiu 2028 Falditas Inc. is a company that is specialized in producing very high-end skirts. Currently, the company produces long and short skirts. Each type of skirt requires a certain amount of processing time distributed as follows: OOST 2H similish916MBtea • Long skirts require 1.2 hours for cutting and 0.7 of hours for sewing. • Short skirts require 0.8 hours for cutting and 0.6 for sewing. miloubo19ers For producing one long skirt, Falditas needs 6 yards of raw materials. This quantity is smaller (4 yards) when it comes to short skirts. These products have very high quality and their price reflects that after taking costs into consideration, the marginal profits are $190 and $150 for long skirts and short skirts, respectively. or doua ni gnola los originalnas al yngmo (1) (s do) cognition to or llw worl bonomolami vartoons al 1

Answer 1

The above set of questions can be answered using the above given data only. We need not to re-run any model again.

(a) Marginal Profit on Long Shirt changed to $210:

As we can see that in the first table allowable increase for the L units is 35 units, we need not to do any changes in the output. Allowable increase here means that by how much we can increase the cofficient of L units i.e. marginal profit on L units such that our final output won't change. Any change after this range would make this output obsolete and we need to re - run the above model only to get the results. Since we are changing it by only 20, thus, our this results would prevail.

New Optimal Profit = Optimal Profit Earlier + Change in Profit (Change in Marginal Profit on L * L units)

New Optimal Profit = $40,900 + (210 - 190) * 100

New Optimal Profit = $42,900

(b) Material Changes:

In case of Material, we can see the 2nd table to get more insights. Against Materials, allowable increase is 133.33 which means we can increase our material by 133.33 yards more without affecting our results. So, if material is available we can go ahead with it but for not more than 133.33 because then our results might change.

But here, we also need to given due consideration to the price which we might pay for this material acquisition. As per that table, Shadow Price for material is $34.5 which means we would be better off if we can acquire materials for less than that amount. If we pay more than that for acquiring then we might get sub - optimal results.

In this case, we are getting material for $8/yard, thus we should go ahead with it but for quantity not more than 133.33, otherwise we would need to re - run our model and then $8 might be expensive. So, upto 133.33 yards @ $8/ yard is good deal. We would be even willing to pay more for this extra material.

How much more = Shadow Price - Deal Price

How much more = 34.5 - 8 = $26.5 / yard.

We would be even willing to pay $26.5 more for 1 yard of material.

(c) Minimum Requirement for Long Skirts:

For long skirts, allowable decrease is 100 units. It means even if reduce the amount of Long skirts produced by 100 units, it won't change our results. So, if the minimum requirement of long skirts is reduced to 75 units only, we need not to change our model. Our existing model would work. The amount of gain that we would get can be determined by the shadow price of it. Its shadow price is negative, it means that if this requirement is reduced by even 1 unit, we would gain $35 and vice - versa.

Gain on reducing minimum requirement for Long Skirts = Shadow Price * Number of Units reduced

Gain on reducing minimum requirement for Long Skirts = 35 * 25 = $875.

Overall Optimal Profit = $40900 + $875 = $41775.