i don't clearly understand questions 1 and 2. so the question have to be A+f???

When he was young, Captain Conundrum mowed lawns on weekends to help pay his college tuition bills. He charged his customers according to the size of their lawns at a rate of 5¢ per square foot and meticulously kept a record of the areas of their lawns in an ordered list:
A = (200, 300, 50, 50, 100, 100, 200, 500, 1000, 100)

He also listed the number of times he mowed each lawn in a given year, for the year 1988 that ordered list was
f = (20, 1, 2, 4, 1, 5, 2, 1, 10, 6)

1. How much did Captain Conundrum earn from mowing lawns in 1988? Write an expression for this amount in terms of the vectors A and f.
2. Suppose Captain Conundrum charged di�fferent customers di�fferent rates. How could you modify the expression in question 2 to compute the Captain's earnings?

earnings = 0.05 A•f

A+f is meaningless, since you can't add ft^2 and n. A•f computes the total ft^2 mowed.

For various earnings, you'd also need a vector of rates.

Not sure how to do that with just vector operations. Say the rates were
0.05, 0.10, 0.07, 0.12, 0.05, 0.08, 0.13, 0.09, 0.10, 0.11

The calculation might look like this:

10
∑ A(i)*r(i) dot f
i=1

Can't think right off how to use vector algebra to do an element-by-element multiply and produce another vector.

thank u so much steve. i have trouble with word problems. now i understand.

Let's break down the questions:

1. To determine how much Captain Conundrum earned from mowing lawns in 1988, we can use the information given in the ordered lists A and f. The list A represents the size of each lawn in square feet, and the list f represents the number of times Captain Conundrum mowed each lawn in 1988.

To calculate the total earnings, we need to multiply the rate per square foot (5¢) by the product of the size of each lawn and the number of times it was mowed.

The expression to calculate the earnings can be written as follows:
Earnings = (A[1] * f[1]) + (A[2] * f[2]) + ... + (A[n] * f[n])

In this expression, A[i] represents the size of the ith lawn, and f[i] represents the number of times the ith lawn was mowed. The sum extends to n, which is the total number of lawns.

2. In question 2, it is stated that Captain Conundrum charged different customers different rates. To compute the Captain's earnings in this scenario, we need to modify the expression from question 1.

Instead of using a fixed rate per square foot, we would need a corresponding rate for each lawn. Let's assume we have another vector r, which represents the rate charged for each lawn. The dimensions of vector r would match the dimensions of vectors A and f, such that r[i] represents the rate for the ith lawn.

The modified expression to calculate the earnings (when charging different rates) would be:
Earnings = (A[1] * f[1] * r[1]) + (A[2] * f[2] * r[2]) + ... + (A[n] * f[n] * r[n])

In this expression, r[i] represents the rate for the ith lawn, A[i] represents the size of the ith lawn, and f[i] represents the number of times the ith lawn was mowed. The sum extends to n, which is the total number of lawns.

By using this modified expression, we can calculate the earnings for Captain Conundrum when charging different rates for each lawn.