Madison Finance has a total of $22 million earmarked for homeowner loans and auto loans, where x is homeowner loans in millions of dollars and y is auto loans in millions of dollars. On the average, homeowner loans have a 8% annual rate of return, whereas auto loans yield a 13% annual rate of return. Management has also stipulated that the total amount of homeowner loans should be greater than or equal to 4 times the total amount of automobile loans. Determine the total amount of loans of each type Madison should extend to each category to maximize its returns P in millions of dollars. Maxmize P=total loansdistributtion of loans

Maximum returns = $1,980,000

x = Homeowner loans = $17,600,000

y = Auto loans = $4,400,000

Madison should extend $17,600,000 in home owners loans and $4,400,000 in auto loans in order to have a maximum return of $1,980,000

Step-by-step explanation:

From the question we are told that:

Madison Finance has a total of $22 million earmarked for homeowner loans and auto loans, where x is homeowner loans in millions of dollars and y is auto loans in millions of dollars.

On the average, homeowner loans have a 8% annual rate of return, whereas auto loans yield a 13% annual rate of return.

We have the equation:

Maximum Return = 8% × x + 13% × y

= 0.08x + 0.13y

We are told in the question that

Management has also stipulated that the total amount of homeowner loans should be greater than or equal to 4 times the total amount of automobile loans.

Hence,

x ≥ 4y

So:

x + y = $22,000,000

4y + y = $22,000,000

5y = $22,000,000

y = $22,000,000/5

y = 4,400,000

x = 4y

x = 4(4,400,000)

x = 17,600,000

Maximum Return = 0.08x + 0.13y

= 0.08 × 17,600,000 + 0.13 × 4,400,000

= $1,980,000

Therefore, Madison should extend $17,600,000 in home owners loans and $4,400,000 in auto loans in order to have a maximum return of $1,980,000

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2