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A cook has a kitchen at the top of a hill, where she can prepare rotis. Each roti costs one rupee to prepare. She can sell rotis for two rupees a piece at a stall down the hill. Once she goes down the steep hill, she can not climb back in time make more rotis.

Suppose the cook can hitch a quick ride from her stall downhill back to the kitchen uphill, by offering a paan to a truck driver. If she starts at the top with $P$ paans and $1$ rupee, what is the minimum and maximum amount of money she can have at the end?

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(a) $\mathrm {R-M + 25}$.

Here  $\mathrm{M\le R}$ is the sum total of rotis made.

$\mathrm {S \le M}$ are the total rotis sold.

$\therefore$ The set of possible values: ${0, 1, 2, \cdots , \mathrm {2R}}$

(b) By preparing $1$ roti and doing nothing else, minimum Rs $=0$.

Maximum rupees $=\mathrm {2P + 1}$

She can make her first roti and then sell for the $2$ Rs.

Total trips she can make to the kitchen $=\mathbf P$ which doubles her money with each trip.

by Boss (19.2k points)