A toy company is planning to expand its operations by buying a new machine. They have short-listed two machines, A & B, based on the quality parameters, maintenance requirement, ease of operations etc. The production cost for each of these machines, for different production ranges is as shown in the table below. Answer the questions based on the data given. (All Costs are in Rs.)

1. If the demand varies between 600-1000 units, which machine would incur the least cost?

a) Machine A b) Machine B c)Both will incur the same cost d) none of these

Sol. d)

Let x be the number of units produced, x lies between 600 and 1000.

In the given range, the total cost of machine A is = 1000+ 2x and cost of machine B = 1200+1.75x

At x=600, the cost of machine A= 2200 and B = 2250;

At x=800, the cost of machine A= 2600 and B = 2600;

At x=1000, the cost of machine A= 3000 and B = 2950;

Thus, we see that Machine A has a lower cost for production between 600 and 800, while B has a lower cost of production between 800 and 1000 units. While both have equal cost at 800 unit production.

Thus, we cannot say which is better for the given range, until further information is given.

2. Which of the following is true?

I. It is favourable to buy machine A if the toy demand is more than 2000 units.

II. Total cost of making 1500 units of toys by the machines A and B differ by Rs. 175

a ) Only I b ) Only II c) both I & II d) None

Sol: b) For the production range of 2000 and above, cost of A is = 1600+ 1.6x;

and for machine B = 1800+1.5x

At x=2001, Cost of A=4810.6 and B=4801.6

Now, we can see that although the fixed cost of Machine B is more than that of machine A, the total cost of production is the same at x=2001. As we keep increasing the unit of production, the cost of A would increase more than that of B (B has less per unit variable cost).

So, it is favourable to buy machine B. Thus I is false.

II. Cost of making 1500 units by machine A=4200, and B = 4025. The difference in the cost = 175.

Thus, II is True.

3. What is the minimum per unit cost of production for these machines?

a) 2.24 b) 2.4 c)2.22 d)2.45

Sol: b)
The per unit cost of production for a machine = Variable per unit cost + (Fixed Cost/Units being produced)
Let us call it TC = v + (f/x)
Now, For TC to be minimum in any range, f/u should be minimum => u should be maximum.
Thus, we can calculate the costs at the end of each range for both machines, as shown in the table.
Thus the minimum per unit cost will be 2.22
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