cost of x tables
= [160-.5(x-250)]x for x>/=250
c = 160 x + 125 x - .5 x^2
c = 285 x - .5 x^2
dc/dx = 285 - x
max when x = 285
then c = .5*285^2 = 40,612.50
and c = 0 when x = 0 of course but also when x = 285*2 = 570
Your firm offers to deliver 250 tables to a dealer, at $160 per table, and to reduce the price per table on the entire order by 50 cents for each additional table over 250.
Find the dollar total involved in the largest possible transaction between the manufacturer and the dealer; then find the smallest possible dollar amount.
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