A manufacturer produces a product at a cost of $26.80 per unit. The manufacturer has a fixed cost of $500.00 per day. Each unit retails for $37.00. Let x represent the number of units produced in a 5-day period.
Write the profit P as a function of x. (Hint: The profit function is given by P(x) = R(x) − C(x)
p(x) = ________
To determine the profit function, we need to calculate the revenue and cost functions first.
The revenue function represents the total income generated from selling a certain number of units. In this case, the revenue is calculated by multiplying the retail price per unit ($37.00) by the number of units produced (x) in the 5-day period. Therefore, the revenue function is given by:
R(x) = 37x
The cost function represents the total cost incurred to produce a certain number of units, including both the variable cost (cost per unit) and the fixed cost. The variable cost per unit is $26.80, so the cost function is given by:
C(x) = 26.80x + 500.00
Now, we can substitute these functions into the profit function:
P(x) = R(x) - C(x)
P(x) = 37x - (26.80x + 500.00)
P(x) = 37x - 26.80x - 500.00
Simplifying the equation, we get:
P(x) = 10.2x - 500.00
Therefore, the profit function P(x) is given by P(x) = 10.2x - 500.00.