Student Doubts Forum

Problem 44

Problem 44

by Francisca Mendes Pereira -
Number of replies: 1

Hello!

I am not quite sure about how to do this exercise.

For 44.1, I obtained the optimal production mix by checking the mix that exhausts manufacturing hours, considering internal demand is always satisfied first.

I did x*1 + (x/2)*3 + (x/2)*2 = 200 000, where x is the amount of mill produced. I obtained x = 57 142.857. Then, the optimal production mix is 57145 units of milk (57142 + 3 units produced with the remaining manufacturing hours), 28 571 units of natural yoghurt and 28 571 units of fruit yoghurt.

Then in 44.2, I obtained a net profit for the order of -5 500.

To do this I did: 50 500 - 23 000 (variable cost) - 20 000 (assuming production of milk remains the same and 20 000 units are removed from the external market to be used internally - loss of 1€ * 20 000 units) - 8000 (referring to the loss of the contribution margin from the 5000 units of natural yoghurt) - 5000 (corresponding to the loss of contribution margin from 5000 units of fruit yoghurt, because natural yoghurt is fully used in fruit yoghurt production, so a decrease in the production of natural yoghurt reduces the fruit yoghurt). 

I got to the decision of not accepting the order, but the incremental profit presented in the solutions is -4250.

Is it possible to clarify whether the computations I made for 44.1 are right and what I did wrong in obtaining incremental profit in 44.2?

Thanks in advance!

In reply to Francisca Mendes Pereira

Re: Problem 44

by Pedro Pinto da Silva Perdigão -
Hello Francisca,

For 44.1 what you did is absolutely right. You can do that because Fruit Yoghurt is the product that maximizes the profit per Mh. You could've used the actual machine hours that each product consumes throughout its whole production process, meaning:

  • Milk -> 1Mh
  • Natural yoghurt -> 5Mh (3Mh from itself and 2Mh that you need to produce the milk used)
  • Fruit yoghurt -> 7Mh (2Mh from itself and 5Mh from the 1 unit of natural yoghurt used)
By finding then the cost per unit of each of the products produced and knowing each contribution margin, you would find that fruit yoghurt ranked 1st amongst the 3 products. Since external demand is 50.000, you would try to meet its demand. But 200.000Mh / 7Mh = 28 571 units, which is the same number you found.

For 44.2, I just don't agree with the last 5000 you mention - in this exercise, we're departing from the situation initially described in the table, therefore the company will remove the units of natural yoghurt that are being used in external demand only. Therefore, production of fruit yoghurt will not change. I do not agree with the value presented in the solutions (-4250), I think it should be -500 instead.

Good study!