Question

Arlington is the financing of two capital improvement projects to prepare for a third World Series. They are (i) street paving in central Arlington and (ii) the improvement of traffic signal lights and street signs in central Arlington. These two projects will cost a total of $400 million and will be funded by a loan from a bank and a loan from an insurance company. The bank will loan any amount of money at the interest rate 3%. The insurance company will loan no more than $300 million at the interest rate 2%. The insurance company also requires that its loan be no larger than the bank loan.
(a) Formulate a linear programming problem to determine the amounts the city should get from the bank and the insurance company so as to minimize the simple interest incurred during the first year after getting the loans. Use the variable B to denote the amount to borrow from the bank and the variable I to denote the amount to get from the insurance company. Assume that the loans will be obtained simultaneously and ignore any integer requirement.

(b) Solve your formulation by the simplex method. Note that you can multiply the objective function by 100 to solve for B and I.

Answer 1

SOLUTION:-

I use B as x1 and as x2 ...

So in below solution replace x1 by B and x2 by I

So, optimal solution is

B = 200

I = 200

min value of Z = 10

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