Valley National Bank has $$1$ million in funds to be allocated between home loans, personal loans and auto loans. The annual rates of return for the loans are $7\%$ for home loans, $12\%$ for personal loans and $9\%$ for auto loans. The bank's planning committee has decided that at least $40\%$ of the funds be allocated to home loans.In addition, the planning committee has determined that the amount allocated to personal loans cannot exceed $60\%$ of the amount allocated to auto loans.Question $5$

$10pts$

Assume that Valley National Bank has the original $$1$ million in funds available and that the planning committee agreed to change the requirement that at least $40\%$ of the new funds must be allocated to home loans and allow at least $41\%$ of the funds to be allocated to home loans. $.$ Use the shadow price as quoted on the report. What is the shadow price $(4$ decimals$)?$ What would the new allocation be and what would the change be on the projected return?

Shadow Price

$H$

P

A

$ Return

$$

$$

$$