MacBurger has just opened a fast-food restaurant inBloomington. Currently, i0 customers frequent MacBurger(we call these loyal customers), and N i0 customers frequentother fast-food establishments (we call these nonloyalcustomers). At the beginning of each month, MacBurger mustdecide how much money to spend on advertising. At the endof a month in which MacBurger spends d dollars onadvertising, a fraction p(d) of the loyal customers becomenonloyal customers, and a fraction q(d) of the nonloyalcustomers become loyal customers. During the next 12months, MacBurger wants to spend D dollars on advertising.Develop a dynamic programming recursion that will enableMacBurger to maximize the number of loyal customers thecompany will have at the end of month 12. (Ignore thepossibility of a fractional number of loyal customers.)
MacBurger has just opened a fast-food restaurant in
Bloomington. Currently, i0 customers frequent MacBurger
(we call these loyal customers), and N i0 customers frequent
other fast-food establishments (we call these nonloyal
customers). At the beginning of each month, MacBurger must
decide how much money to spend on advertising. At the endof a month in which MacBurger spends d dollars on
advertising, a fraction p(d) of the loyal customers become
nonloyal customers, and a fraction q(d) of the nonloyal
customers become loyal customers. During the next 12
months, MacBurger wants to spend D dollars on advertising.
Develop a dynamic programming recursion that will enable
MacBurger to maximize the number of loyal customers the
company will have at the end of month 12. (Ignore the
possibility of a fractional number of loyal customers.)
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