Question

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 different customers different rates. How could you modify the expression in question 2 to compute the Captain's earnings?

Answer 1

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.

Answer 2

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