A company is planning to manufacture snowboards. The fixed costs are $100 per da

Question

A company is planning to manufacture snowboards. The fixed costs are $100 per day and total costs are $4900 per day at a daily output of 20 boards. A. Assuming that the total cost per day, C(x), is linearly related to the total output per day, x, write an equation for the cost function. C(x) B. The average cost per board for an output of x boards is given by C(x)-C(x)/x. Find the average cost function. C(x) C. Sketch a graph of the average cost function, including any asymptotes, for 1 sxs30. Choose the correct graph below. O A ? ?. ??. O D. 30 30 30 30 D. What does the average cost per board tend to as production increases?

Explanation / Answer

Total cost = Fixed Cost + Variable cost per unit * number of units
Substituting the values we get
4900 = 100 + 20 * x where 'x' is the variable cost per unit
4900 = 100 + 20x
x= 4800 / 20 = 240
Thus, the cost function is = 100 + 240* y where 'y' is the number of units


Average cost function = total cost function / number of units
= 100 + 240y / y = 100/y + 240  
Thus, average cost function is = 100/y + 240

The value converges to 240 as y tends to increase to a very large number; Hence option C is the right graph

D) As production increases, it can be seen from the graph of 'C' option is question C that the average cost decreases and converges to 240 as number of units increase

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