I need help on the following question: In order to maintain its competitiveness

Question

I need help on the following question:

In order to maintain its competitiveness among other oyster sauce producers in the Malaysian market, the production manager of Maggi Oyster Sauce Malaysia is interested to assess the cost effectiveness of the company’s production. The total costs are given by the following relationship:

         TC = 0.10Q3 – 3Q2 +60Q + 250

         where     TC =    total cost                        Q   =    quantity of oyster sauce produced (in ‘000)

Question: What is the marginal cost when 10,000 bottles of oyster sauce are produced? Does it the same if the number of production increase to 11,000 bottles? As the production manager, what should you do?

here's my working method:

The following are steps to find the value or marginal cost and the action required by the production manager based on the analysis of the marginal cost value when output of Q is 10,000 bottles and when Q is increased to 11,000 bottle:

         Solution Step 1: Find the value of MC at Q=10,000 bottles

Solution Step 2: Find the value of MC at Q=11,000 bottles

Solution Step 3: Analyze the result and propose action that should be taken by the production manager

         Solution Step 1

         The value of MC at Q=10,000 bottles can be calculated using the formula of MC = 0.30Q2-6Q+60 derived from answer in Task 4 para 2 (Solution Step 1)

         Since the quantity of oyster sauce produced is in ‘000, we insert the value of Q=10 into the formula:

         MC = 0.30Q2-6Q+60

                = 0.30(10)2 -6(10)+60

                =0.3(100)-60+60

                =30

Therefore, at Q=10, MC =30

Solution Step 2

                    The value of MC at Q=11,000 bottles will also be calculated using the formula of MC = 0.30Q2-6Q+60 derived from answer in Task 4 para 2 (Solution Step 1)

Insert the value of Q=11 into the formula of MC:

         MC = 0.30Q2-6Q+60

                = 0.30(11)2 -6(11)+60

                =0.3(121)-66+60

                =36.3-66+60

                =30.3

Therefore, at Q=11, MC =30.3

                    Solution Step 3:

Based from the Solution Step 1 and Solution Step 2, it was found:

At Q=10, the MC = 30

At Q=11, the MC=RM30.3

Going back to the definition, MC is the cost added by producing one (1) additional unit of a product or service. Based from the above calculation, it was found that for one (1) additional unit of oyster sauce produced, the cost of production increases by RM0.30. In other words, Maggi Oyster Sauce Malaysia have to increase cost in order to produce an additional unit of oyster sauce.

My question, i now know that the MC cost to produce 1 more oyster increases by RM0.30 per bottle, but on the perspective of the company production manager, I'm stuck. I know that MC will enable the company to make decision whether to contine production, or increase/decrase its variable input to reduce the cost but i just don't know how to answer. Appreciate your help with regards to this.

Explanation / Answer

Consider the given problem here the “TC” is given by.

=> TC = 250 + 60*Q – 3*Q^2 + 0.1*Q^3, => MC = 60 -6*Q + 0.3*Q^2. So, at “Q=10”, “MC=30” and at “Q=11”, “MC=30.3”.

Now, the slope of “MC” is “d(MC)/dQ = -6 + 0.6*Q”, => at “Q=10”, => d(MC)/dQ = -6 + 0.6*10 = 0” and at “Q=11” the slope is “d(MC)/dQ = 0.6 > 0. So, at “Q=10” the “MC” is minimum and at “Q=11” the “MC” is increasing. So, here we can see that the “MC” for “10,000” and “11,000” are not same there is difference of “0.3”.

Now, if we talk about the production decision then the production decision depends on the actual price of the good. So, if the actual price is “P > 30.3“, then it is optimum to increase “Q”. Since as we know that at the optimum “P” must be equal to “MC” and at that point “MC” must be upward rising.

So, if “P=30.3” then optimum “Q” is “11,000”. If “P > MC = 30.3”, => it is optimum to increase production. Since if “P > MC”, => return from additional production is more than the cost of production of the additional unit, => it is more profitable to increase production. Now, if “P < 30.3”, => it is optimum to reduce production. Since if “P < MC”, => return from additional production is less than the cost of production of the additional unit, => it is more profitable to reduce production.

So, the decision to choose “Q” depends totally on “P”.

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