Question

A food truck caters an event attended by 100 guests. Every guest orders one of two possible dishes: a salad or a turkey plate. The price of each meal decreases as more of that particular type are ordered. The price of a salad is $10.00 minus $0.05 for each salad ordered. The price of a turkey plate is $12.00 minus $0.01 multiplied by the square of the number of turkey plates ordered. Guests pay for their meal only after everyone has placed their order. Using differentiation, find the maximum revenue for the food truck. Remember that the number of meals is a positive integer. Round revenue to the nearest cent. maximum revenue: $

Answer 1

Solutions Given that A food truck caters an event attended by 100 guests. There are two possibie dishes: Salad, turkey plate. The price of salad is $10.00 minus $005 for each salad The price of turkey plate is $12.00 minus $0.01. - price of each Salad = 10-(0.05)X. consider a guests Order salad and 100-1 guest order turkey plate. Price of each turkey plate = 12-100-x) (0.01) = 12-1+0.012 - 11+0.01% :. Revenue = a (10-10-057x] +(100-x) (il +0.011*] RU)= (10x -0.05%] + [1100 + 2) + (-11% - 0.01m] - 1100-11++10X-01012 -0.05 RA). = 1100 -0.06 ł Rah) = - 20.061. R(W) = o-0.12% = -0.127 for maximum revenue RR=0 -0.12 2=0

R a) = -0.12 (1) = 0.12 20 RO<O when a=0 R" doko we get maximum Revenue. Maximum Revenue Rois o [10-10.05) 0] +(100-0) (1 + (0.01.top 60): 0 +(\oo] [u] 80) = 11 00 .: Maximum Revenue = $(10900