A toilet manufacturer has decided to come out with a new and improved toilet. The fixed cost for the production of this new toilet line is $16,600 and the variable costs are $63 per toilet. The company expects to sell the toilets for $160. Formulate a function C(x) for the total cost of producing x new toilets and a function R(x) for the total revenue generated from the sales of x toilets. How many toilets need to be sold to break even?

C(x)=16600+63x

R(x)=160x

Break-even Point, x=172

Step-by-step explanation:

Let x be the number of Toilets Produced.

Fixed cost = $16,600

Variable costs = $63 per toilet.

Total Cost, C(x)=16600+63x

The company expects to sell the toilets for $160.

Selling Price Per Toilet=160

Total Revenue for x Toilets, R(x)=160x

Next, we determine the break-even point.

The break-even point is the point where the Cost of Production equals Revenue generated.

i.e. C(x)=R(x)

16600+63x=160x

16600=160x-63x

16600=97x

x=171.13

The company needs to sell at least 172 Toilets to break even.

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