linear programming to determine how Alexis can maximize her cash on hand at the
ID: 3027794 • Letter: L
Question
linear programming to determine how Alexis can maximize her cash on hand at the end of April 49sAt the beginning of month 1, Finco has $400 in cash. At the beginning of months i, 2, 3, and 4, Finco receives certain revenues, after which it pays bills (see Table 78 Any money left over may be invested for one month at the interest rate of 0.1% per month; for two months at 0.5% per month; for three months at 1% per month; or for four months at 2% per month. Use linear programming to determine an investment strategy that maximizes cash on hand at the beginning of month 5 50 City 1 produces 500 tons of waste per day, and city 2 produces 400 tons of waste per day. Waste must be incinerated at incinerator l or 2, and each incinerator can process up to 500 tons of waste per day. The cost to incinerate waste is $40/ton at incinerator and $30/ton at 2 TABLE 78 Month Revenues (S) Bills (S) 400 600 800 500 300 500 300 250 Based on Charnes and Cooper (1955) s Based on Robichek, Teichroew, and Jones (1965)Explanation / Answer
In table 78 revenues and bills are given
for constrains
Cash available in month t = Investment in month t + bills paid in month t. This is called as balanced constraint
Let Xij = the amount invested at the begining of month " i " that matures at the end of month " j ".
The objective is to maximize the cash at end of month 4.
therefore Max 1.08x14 + 1.03x24 + 1.01x34 + 1.001x44 .
subject to x11 + x12 + x13 + x14 + 600 = 800 (400 + 400)
x22 + x23 + x24 + 500 = 800 + 1.001x11 ( 800 + 1.001x11 = principle + interest returned on the money for one month at the begining of month 1)
x33 + x34 + 500 = 300 + 1.01x12 + 1.001x22 .
x44 + 250 = 300 + 1.03x13 + 1.01x23 + 1.001x33
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