1. An expression that describes the price of each table, based on the number of reductions, is 95 –2x, where x represents the number of $2 reductions in price. Write a similar expression to describe the number of tables the carpenter can expect to sell, based on the number of reductions.
B. Write an equation to describe the carpenter’s income as a product of the price of each table and the expected number of tables sold.
C. The carpenter hopes to earn $3600 to pay for his time, materials, and sales booth, as well as make a small profit. Determine the number of $2 reductions he can apply to the price of the tables to make $3600.
D. How many reductions will produce maximum income? Indicate the number of tables sold and the price of each one when maximum occurs.
Please go back and read Writeacher's response to you.
We're not fooled by your different names on the seven posts.
A. To write a similar expression to describe the number of tables the carpenter can expect to sell based on the number of reductions, we need to consider a few things. The expression for the price of each table is given as 95 - 2x, where x represents the number of $2 reductions in price. In this case, the price of each table decreases as the number of reductions (x) increases. Therefore, we can assume that the number of tables sold will increase as the price decreases.
Let's say the number of tables the carpenter can expect to sell is y. To represent this relationship, we can write the expression as:
y = f(x)
B. To write an equation to describe the carpenter's income as a product of the price of each table and the expected number of tables sold, we can use the expressions we have. The price of each table is given as 95 - 2x, and the number of tables sold is represented by y. The equation for the carpenter's income (I) can be written as:
I = (95 - 2x) * y
C. To determine the number of $2 reductions the carpenter can apply to the price of the tables to make $3600, we need to set up an equation. We know that the carpenter's income (I) should be $3600. Using the equation from Part B, we can write:
(95 - 2x) * y = 3600
Since we don't have the value of y, we need to isolate it first. Dividing both sides of the equation by (95 - 2x), we get:
y = 3600 / (95 - 2x)
Now, we can apply different values for x and find the corresponding value of y that satisfies the equation. This will give us the number of $2 reductions the carpenter can apply to the price of the tables to make $3600.
D. To find the number of reductions that produce maximum income, we need to understand that the income is a product of the price of each table and the number of tables sold.
From Part A, we have the expression for the number of tables sold as y = f(x). To find the maximum income, we have to consider the maximum value of y.
By identifying the maximum value of y, we can then determine the corresponding value of x (the number of reductions) and use it to find the price of each table.
To find the maximum value of y, we can take the derivative of the expression for y with respect to x, set it equal to zero, and solve for x.
After finding the x value that maximizes y, we can substitute it into the expression for the price of each table (95 - 2x) to find the price at maximum income.
Note: Without additional information provided about the specific function f(x), it is not possible to determine the exact values for the number of tables sold and the price at maximum income.