Question 1165819
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Here are alternative methods for solving each of the two parts of the problem.<br>
The graph of the cost function is a parabola, with its minimum value when the number of chairs ordered is {{{(-(-14))/2=7}}}<br>
a. Find x such that the cost of each chair is the same as when Mr. Lim
ordered 5 chairs.<br>
Since the graph is symmetric about the axis of symmetry x=7, the cost will be the same for 9 chairs as it is for 5 chairs.<br>
ANSWER: 9 chairs can be ordered for the same cost as 5 chairs<br>
b. Find the number of chairs in a batch he needs to orders such that the cost
per chair is less than $45.<br>
The minimum cost, when 7 chairs are ordered, is {{{7^2-14(7)+80=31}}}<br>
Because the leading term of the cost function is {{{x^2}}}, the cost will differ from the minimum cost of $31 by n^2 when x differs from 7 by n.  We need the cost to be less than $45, which differs from the minimum cost of $31 by $14.  Since 3^2 is less than 14 and 4^2 is greater than 14, the number of chairs that can be ordered for less than $45 can differ from 7 by at most 3.<br>
ANSWER: Between 4 and 10 chairs can be ordered for a cost less than $45<br>