Answers
a.
Let's consider
x = Loan amount disbursed as home loans (in Millions)
y = Loan amount disbursed as auto loans (in Millions)
Objective Function:
Total return from loaning activity = 10%*x + y*12%
Total return from loaning activity = 0.1*x + 0.12*y
Maximize P= 0.1*x + 0.12*y ............ as Madison Finance wants to maximize return on loaning activity
Constraints:
x + y =18 .............Constraint on the total loan amount to be disbursed
x>=4*y ............. Contraint on the distribution of loan as homeowner loans should be greater than or equal to 4 times the total amount of automobile loans
x,y>=0 .......Non-negativity constraint as selected variables cannot be negative
b.
Let's consider
x = Ounces of Food A
y = Ounces of Food B
Objective Function:
Total cholesterol content = 2*x + 5*y as each ounce of A has 2 mg of cholesterol and each ounce of B has 5 mg of cholesterol
Minimize C = 2*x + 5*y ............as nutritionist wants to minimize cholesterol content
Constraints:
30*x + 25*y >= 420 ..........Constraint on minimum calcium requirement
2*x + 0.5*y >= 15 ..........Constraint on minimum iron requirement
1*x + 5*y >= 45 ..........Constraint on minimum vitamin C requirement
x,y >=0 .......Non-negativity constraint as selected variables cannot be negative
c.
Let's consider
x = Money invested in project A
y = Money invested in project B
Objective Function:
Total return from investment activity = 11%*x + y*13%
Total return from investment activity =0.11*x + 0.13*y
Maximize P= 0.11*x + 0.13*y ............ as financier wants to maximize return on investment activity
Constraints:
x+y = 400,000 ..........Constraint on the amount to be invested in projects A and B
y<= 35%*(x+y)
y <= 0.35*x + 0.35*y
0.65*y<=0.35*x .............Constraint on amount to be invested in project B as it is riskier than project A
x,y>=0 .......Non-negativity constraint as selected variable cannot be negative
.