Final Answer:
The revenue generated by selling x electric drills per month at a selling price of p dollars each is given by R(x) = px. The profit function, P(x), can be represented as P(x) = R(x) - C(x), where C(x) is the total cost function. Hence, the profit function for Manny's Tools LLC is P(x) = px - (64000 + 70x).
Step-by-step explanation:
Manny's Tools LLC's revenue, which is the income generated from selling x electric drills per month, is calculated by multiplying the number of drills sold (x) by the selling price per drill (p), yielding the revenue function R(x) = px.
The total cost function, C(x), represents the expenses incurred by the company. In this scenario, the total monthly cost (C(x)) of manufacturing x electric drills is given as C(x) = 64000 + 70x, which includes fixed costs of $64,000 and variable costs of $70 per drill.
The profit, P(x), is the difference between revenue and cost. It is obtained by subtracting the total cost (C(x)) from the revenue (R(x)), thus giving the equation P(x) = R(x) - C(x). Substituting the expressions for revenue and cost into this formula results in P(x) = px - (64000 + 70x), representing the profit function for Manny's Tools LLC.
This profit function allows the company to assess its profitability at different levels of production (x drills manufactured and sold) and selling prices (p dollars per drill). By maximizing this profit function or analyzing it with respect to different variables, the company can make informed decisions regarding pricing strategies, production levels, and overall profitability.