How do you set up the inequalities etc for this problem?
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A bank is attempting to determine where its assets should be invested during the current year. At present, $500,000 is available for investment in bonds, home loans, auto loans, and personal loans. The annual rates of return are:
Bonds=10%, Home Loans 16%
Auto Loans 13%, Personal Loans 20%.
Restrictions:
The amount invested in personal loans cannot exceed the amount invested in bonds.
The amount invested in home loans cannot exceed the amount invested in auto loans.
No more than 25% of the total amount invested in auto loans may be invested in personal loans.
Help the bank maximize the annual return on its investment portfolio by formulating the linear program.
Please use w,x,y,z for variables so I can follow along... Thank you for helping out.
How do you set up the inequalities etc for this problem?w = Bond Investment
x = Home Loan Investment
y = Auto Loan Investment
z = Personal Loan Investment
Eq.#1: 0.10w + 0.16x + 0.13y + 0.20z = 500000
Eq.#2: z <= w
Eq.#3: x <= y
Eq.#4: z <= 0.25y
How do you set up the inequalities etc for this problem?Define the following
w is the amount invested in bonds,
x is the amount invested in home loans.
y is the amount invested in auto loans.
z is the amount invested in personal loans.
w+x+y+z <= 500,000
z<=w -----> 1st restriction
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