Operating a Tour ServiceDate: 5/21/96 at 16:47:58 From: Anonymous Subject: Calculus You operate a tour service that offers the following rates: i) $200 per person if 50 people (the minimum number to book the tour) go on the tour. ii) For each additional person, up to a maximum of 80 people total, everyone's charge is reduced by $2. It costs you $6000 (a fixed cost) plus $32 per person to conduct the tour. How many people does it take to maximize your profit? Date: 6/1/96 at 15:15:6 From: Doctor Anthony Subject: Re: Calculus Let x = number people you take. Cost per person will be 200-2(x-50) = 200-2x+100 = 300-2x Total income to you = x(300-2x) = 300x - 2x^2 Total costs to you = 6000 + 32x Profit = 300x - 2x^2 - 6000 - 32x = 268x - 2x^2 - 6000 Differentiate to find a maximum point dP/dx = 268 - 4x = 0 for max point. So x = 268/4 = 67 So you should take 67 people to maximize your profit. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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