Question

The amount of money Jose’s lawn mowing company earns for a contract is given by the function , where is the number of acres that the client needs mowed and is the revenue generated. The amount of money a Green Grass lawn mowing company earns for a contract is given by the function , where is the number of acres that the client needs mowed and is the revenue generated. The two companies decided to merge and in order to merge they have to add their contract functions.

Answer 1

To calculate acres left to mow after a certain number of hours, plug in hours worked into the function ŷ = 1350 - 1.2x. For the profit calculation, the farm's total revenue equals total costs, resulting in zero profit. Income in a market economy comes from wages, rent, interest, and dividends, based on ownership of production means.

Step-by-step explanation:

Mowing the Properties Function

The function for the rate at which one person can mow is given by ŷ = 1350 - 1.2x, where x is the number of hours worked and ŷ represents the number of acres left to mow. To find the acres left after a certain number of hours, we simply plug in the value of x into the function.

• After 20 hours: ŷ = 1350 - 1.2(20) = 1350 - 24 = 1326 acres left to mow.
• After 100 hours: ŷ = 1350 - 1.2(100) = 1350 - 120 = 1230 acres left to mow.
• To find out when all the lawns are mowed, or when ŷ = 0, we set up the equation: 0 = 1350 - 1.2x. Solving for x gives us x = 1350 / 1.2 = 1125 hours.

For the revenue and cost situation, where profit is calculated as total revenue - total costs, in the given example, the firm is making zero profit as:

profit = (75)($2.75) - (75)($2.75) = $0

In terms of marketplace income, individuals earn based on the ownership of the means of production, and their income typically comes from wages, rent, interest, and dividends. This is particularly true in a market economy such as the United States.