Question

A company sells washing machines for $340 each. To produce a batch of n washing machines, there is a cost of $249 per washing machine and a fixed or setup cost of $14,600 for the entire batch. Determine a function that gives the profit in terms of the number of washing machines produced. What is the least number of washing machines the company can sell in order to have a profit of $14,000?

Answer 1

Revenue funtion, R(n) = p * n, (where p is selling price per item and n is number of items.)

Cost function, C(n) = F + Vn, (where F is fixed or set up cost, V is variable cost price per item and n is number of items)

Profit fuction, P(n) = R(n) - C(n)

In the given problem,

Selling price per item (p) = $ 340

Therefore R(n) = 340 n ....................Equation(1)

Cost price per item = $249 and Fixed or set up cost = $ 14,600

Therefore C(n) = F + Vn = 14,600 + 249 n .................Equation (2)

Using equation 1 and 2 we can find profit fucntion

Therefore P(n) = R (n) - C(n) = 340 n - 14600 - 249 n = 91 n - 14600

Thus the profit fuction, P(n) = 91 n - 14600 ................Equation (3)

Now we find the number of washing machines to get the profit of 14,000

Put the profit value 14,000 in the profit function, that is in equation (3)

So we get 14,000 = 91n - 14,600

91 n = 14,000 + 14,600

n = 28,600 / 91

n = 314.28

Therefore the company can sell at least 315 number of washing machines in order to have a profit of $14,000.

(We round figure 314.28 to next integer 315 because we do not get profit $14,000 with 314 washing machines)