Suppose Spoon World Inc manufactures electric spoons with a

Suppose Spoon World Inc. manufactures electric spoons with a fixed production cost of $700 and a marginal cost per spoon of $12. The company sells each spoon for $40. are both linear functions, find the following: the cost function the revenue function the values (x, y) for the break-even point, the point at which cost equals revenue

Solution

Let the number of electric spoons manufactured = x.

(a) Cost function ,

C(x) = variable cost + fixed cost = 12*x + 700 = 12x+700

(b) Revenue function,

R(x) = 40*x = 40x

(c) C(x) = R(x)

12x+700 = 40x

Subtract 12x from both the sides,

700 = 28x

Dividing both the sides by 28, we get

x= 25 spoons

Substitute this either in C(x) or in R(x),

R(25) = 40 * 25 = 1000

So break even point, (x,y) = (25,1000)