Hi! I am trying to figure out this practice problem to study for my upcoming midterm. I am having a lot of trouble with this question and if anyone could help me I would really appreciate it. Thank you in advance!
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Ms. Dyer wants to develop an investment strategy to finance her four-year law school education and articling. She will be able to draw upon several sources of funding: a university scholarship, a small inheritance left recently by her grandmother, as well as some RESP funds established by her parents for her when she was young. Naturally, she wishes to have available the largest possible amount of cash upon graduation. She estimates her revenues and expenses as:
Revenues ($1000):
Year 1 – 30
Year 2 – 40
Year 3 – 25
Year 4 – 15
Expenses ($1000):
Year 1 – 10
Year 2 – 25
Year 3 – 25
Year 4 – 12.5
Ms. Dyer has $5,000 in cash right now; assume now is the beginning of year one, and that both her expenses and revenues occur at the beginning of each year. Any money left over in any year can be invested in guaranteed investment certificates (GIC's) for one year at a rate of 1.45%, for two years at 3.73%, for three years at 4.88%, and for four years at 6.98%. She uses the principle
Money invested + Expenses Paid < Revenue + Money Earned from Investment
Formulate an LP model that will maximize the value of Ms. Dyer's GIC's at the end of her fourth year.
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I started to work on the question but have no idea if what I am doing is satisfying the problem or answers what the problem is looking for:
Let 'r' = revenus (in $1000)
Let 'e= expenses (in $1000)
Let x_{i}= amount invested in year i, i= 1,2,...5
Objective function:
Maximize value of GIC's ('v')
V=1.045 X_{i} + 1.0373 X_{ii} + 1.0488 X_{iii} + 1.0488 X_{iv}
Constraints:
(x_{i + }x_{ii +} x_{iii + }x_{iv}) + e < r + v
x_{i, }x_{ii ,} x_{iii , }x_{iv}> 0
I don't know if that is correct or if it will help me solve the problem.