a. Find the value of k in his production.

b. Calculate his initial costs.

c. James sells the rocking horses for $50 each. How many horses will he need to sell before he begins to make a profit?

d. James makes and sells 14 horses calculate his total profit?

e. Why would it be unwise for James to rely on this formula when producing large numbers of rocking horses? Justify your answer with appropriate mathematics

a. $$80=\frac{k}{2+1}$$

$$80=\frac{k}{3}$$

k = 240

to find the value of k, substitute in any pair of numbers from the table

solve for k

c. $$50=\frac{240}{n+1}$$
$$50^{\times(n+1)}=\frac{240}{\cancel{(n+1)}}^{\times\cancel{(n+1)}}$$
50n + 50 = 240
50n = 190
n = 3.8

∴ n = 4

Find the break even point, which is where the costs equal the sales

solve for n

so he will need to sell 4 horses or more as he can’t sell part of a unit

d. Sales: 14 × 50
= $700

Cost = $$\frac{240}{14+1}$$
= $16 per horse

Total cost = 16 × 14
= $224

Profit is sales price – cost price

Profit = 700 – 224 = $476

Find the value of the sales when n = 14, sold at $50 each

Find the cost of making a single horse if he makes 14 horses

find the cost of making 14 of them at $16 each

e. when n gets large C becomes unrealistic as it gets closer to zero and it should be obvious that the cost cannot be zero

an example of making 1000 horses: $$\frac{240}{1000+1}=0.24$$

the formula says that it will cost him only 24 cents to make a horse, and that is a ridiculously small cost. As you make more, soon the number would become so small, it would be practically zero, which is unrealistic