TRAVEL AGENCY. Trieloff Travel is a travel that books both individual travel and

Question

TRAVEL AGENCY. Trieloff Travel is a travel that books both individual travel and group package tours primarily for senior citizens. Jim Trieloff, the owner of the agency, employs himself, his wife, and two other full-time employees working 8 hours per day, 5 days a week. He also employs two half-time workers, giving him a total of 4(40) + 2(20) = 200 worker-hours per week. He estimates that each individual travel package booked nets him an average of $65, whereas each tour arranged nets him $2500. Each individual package usually takes about 3 man-hours to arrange, and each tour package takes 2 people a combined average of 50 man-hours to put together. Because he wants to establish himself primarily as a tour promoter, he will only allocate between 40 and 60 man-hours for handling individual packages. In a typical week, how should Jim allocate his personnel time between working on individual travel packages and group tours to maximize his expected weekly profit? Comment on the meaning of the fractional values. Now, please help Trieloff to build the mathematical model for this problem and solve it using geometric solution.

Explanation / Answer

To maximize

(65/3) x1 + (2500/50) x2

Here x1 is no of hours on individual project and x2 is no of hours on group package

65/3 = Money earned per hour for individual package

(2500/50) = Money earned per hour for group package

we know that x1 +x2 =200

also 40<=x1<=60

on solving we get x1=40 and x2=160

so maximize profit = (65/3) * 40 + (2500/50)*160 = 8866.667 Rs

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