I just need the problem set up...no need to solve. Thanks! Problem 2. [15 points

Question

I just need the problem set up...no need to solve. Thanks!

Problem 2. [15 points] At the beginning of months 1, 2, 3, and 4, the Simplex Company receives certain revenues, after which it pays the bills: Revenues Bills Month 1 $800$600 Month 2$800 $500 Month 3 $300 $500 Month 4 $300 S250 Any money left over may be invested for 1 month at an interest rate of 1%, or for two months at an interest rate of 3%. For example, x dollars invested at the beginning of month 2 becomes 1.01x dollar month 4, depending on how it was invested. Formulate a linear program that determines an investment strategy that maximizes cash orn hand at the beginning of month 5. Clearly define in words what your decision variables represent. In the LP, label each constraint with a keyword for what the constraint corresponds to. You do not need to solve the LP. Do not worry about decision variable integrality. s at the beginning of month 3 or 1.03z dollars at the beginning of

Explanation / Answer

let at the end of the 1st month invest on 1 month and two month plan is x1 and y1 respectively. let at the end of 2nd month investment on 1 month plan and 2nd month plan is x2 and y2 respectively. at the end of 3rd month we invest all savings (assume x3) in 1 month plan only,because we need whole money at the begining of the 5th month not at the last of the 5th month.

so, our objective function that we have to maximize will be as..

0.01x1+0.03y1+0.01x2+0.03y2+1.01x3+50.........(a)

now costraint will be as...

x1+y1<= 200.......(1)

x2+y2 - 1.01x1 <= 300......(2)

x3 = 1.01x2+1.03y1 - 200 .......(3)

now solve the question by big M method......

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