A manufacturer has decided to come out with a new and improved toilet. The fixed cost for the production of this new toilet line is $16,000 and the variable costs are $68 per toilet. The company expects to sell the toilets for $154. Formulate the function C(x) for the total cost of procucing x new toilets and a function R(x) for the total revenue generated from the sales of x toilets.
To formulate the function for the total cost of producing x new toilets, we'll consider both the fixed cost and the variable cost.
1. Fixed cost: The fixed cost remains constant regardless of the number of toilets produced. In this case, the fixed cost is $16,000.
2. Variable cost: The variable cost depends on the number of toilets produced. For each toilet, the cost is $68. Therefore, for x toilets, the variable cost would be 68x.
By adding the fixed cost and variable cost, we can get the total cost function:
C(x) = Fixed cost + Variable cost
C(x) = $16,000 + 68x
To formulate the function for the total revenue generated from the sales of x toilets, we'll consider the selling price of each toilet.
For each toilet sold, the revenue generated would be $154. Therefore, for x toilets, the revenue would be 154x.
So, the total revenue function is:
R(x) = Selling price × Number of toilets sold
R(x) = $154x
So, the functions are as follows:
C(x) = $16,000 + 68x (Total cost of producing x new toilets)
R(x) = $154x (Total revenue generated from the sales of x toilets)
To formulate the function C(x) for the total cost of producing x new toilets, we need to consider both the fixed costs and the variable costs.
Fixed costs:
The fixed cost for production is $16,000. Since this cost does not depend on the number of toilets produced, it remains constant regardless of the number of toilets produced.
Variable costs:
The variable cost per toilet is $68. So, for x toilets, the variable cost would be 68x.
Therefore, the total cost (C(x)) can be calculated by adding the fixed costs and the variable costs:
C(x) = Fixed costs + Variable costs
C(x) = $16,000 + $68x
To formulate the function R(x) for the total revenue generated from the sales of x toilets, we need to consider the selling price per toilet and the number of toilets sold.
The selling price per toilet is $154, and the number of toilets sold is x.
Therefore, the total revenue (R(x)) can be calculated by multiplying the selling price per toilet with the number of toilets sold:
R(x) = Selling price per toilet * Number of toilets sold
R(x) = $154 * x
C(x) = 16,000 + 68 x
R(x) = 154 x