# Mathematical Models Involving Linear Systems

Loser rental charges \$32.00 a day plus 27 cents per mile. lemon leasers \$28.00 plus 30 cents per mile. Most renters drive either fewer than 50 mile or more than 200 miles. I have to start a company that has rates that are less expensive than both of the other two car rentals. Rates must not be less expensive than both of the other companies' rates outside this interval. Must compare my price structure to the other two numerically, algebraically, and graphically. Must compare a fierce advertising campaign, quoting unbeatable prices for trips in this range while minimizing my financial risk and explain why this is true

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...izing my financial risk and explain why this is true

Solution:

Suppose you propose a rental charge of \$x1 a day plus y1 cents per mile if the renter drives t1 miles where t1<50 or t1>50. Then the rental charge for one driver is

x1+y1*t1/100 dollars

where

x1<=28
y1<=27
t1<50 or t1>50

So in order to have unbeatable price with maximum profit. You need to set x1, y1 to be as large as possible yet in the range x1<=28, y1<=27. Thus set x1=28, y1=27

Suppose now you propose a rental charge of \$x2 a day plus y2 cents per mile if the renter drives t2 miles where 50<=t2<=200. Then the ...