11.) A company produces a product for which the variable cost is $12.30 per unit and the fixed costs are $98,000. The product sells for $17.98. Let x be the number of units produced and sold.
a.) the total cost for a business is th sum of the variable cost and the fixed costs. Write the total cost C as a function of the number of units produced.
b.) write the revenue R as a function of the number of units sold.
d.) Write the profit P as a function of the number of units sold.
I know that P=R-C...
c = 98,000 + 12.3 x
r = 17.98 x
a.) The total cost, C, can be written as the sum of the variable cost and the fixed costs:
C(x) = (12.30 * x) + 98,000
b.) The revenue, R, can be written as the product of the selling price and the number of units sold:
R(x) = 17.98 * x
c.) To calculate the profit, P, we need to subtract the total cost from the revenue:
P(x) = R(x) - C(x)
Therefore, P(x) = (17.98 * x) - (12.30 * x + 98,000)
a.) To write the total cost C as a function of the number of units produced, we need to consider both the fixed costs and the variable costs. The fixed costs of the business are given as $98,000, which do not change with the number of units produced. The variable cost is given as $12.30 per unit, so for x units produced, the variable cost would be 12.30x. Therefore, the total cost C can be expressed as:
C(x) = fixed costs + variable costs
C(x) = $98,000 + (12.30x)
b.) The revenue R can be expressed as the selling price multiplied by the number of units sold. The selling price per unit is given as $17.98, so for x units sold, the revenue R can be written as:
R(x) = selling price × number of units sold
R(x) = $17.98x
d.) You correctly stated that profit P is given by the equation P = R - C. Substituting the expressions for R and C from earlier, we get:
P(x) = R(x) - C(x)
P(x) = ($17.98x) - ($98,000 + 12.30x)
P(x) = $17.98x - $98,000 - 12.30x
P(x) = 5.68x - $98,000
Therefore, the profit P can be expressed as a function of the number of units sold (x) as P(x) = 5.68x - $98,000.