. Margaret is planning to invest up to $22,000 in certificates of deposit at City Bank and People’s Bank. She wants to invest at least $2000 but no more than $14,000 at City Bank. People’s Bank does not insure more than a $15,000 investment, so she will invest no more than that in People’s Bank. The interest is 6% at City Bank and 6 12 % at People’s Bank. This is simple interest for one year. How much should she invest in each bank in order to maximize her income? What is the maximum income?

Question

. Margaret is planning to invest up to $22,000 in certificates of deposit at City Bank and People’s Bank. She wants to invest at least $2000 but no more than $14,000 at City Bank. People’s Bank does not insure more than a $15,000 investment, so she will invest no more than that in People’s Bank. The interest is 6% at City Bank and 6 12 % at People’s Bank. This is simple interest for one year. How much should she invest in each bank in order to maximize her income? What is the maximum income?

Answer 1

say she invests

x at City Bank
y at People's Bank
where x and y are in thousands.
Then the constraints are
x+y <= 22
2 <= x <= 14
0 <= y < =15
You want to maximize p = 0.06x + 0.0612y

so graph the region and evaluate p(x,y) at the vertices.