Question

7. Tickets for a concert are cheaper when purchased in quantity. The first 100 tickets are priced at $27 each, but each additional block of 100 tickets purchased decreases the cost of each ticket by 50¢. How many blocks of tickets should be sold to maximize the revenue? (Round your answer to the nearest integer.)
blocks

8. A rain gutter is formed by bending up the sides of a 30-inch-wide rectangular metal sheet.

(a) Find a function A that models the cross-sectional area of the gutter in terms of x.

A(x) =

(b) Find the value of x that maximizes the cross-sectional area of the gutter.

x = in

(c) What is the maximum cross-sectional area for the gutter?

in^2

Answer 1

7. Tickets for a concert are cheaper when purchased in quantity. The first 100 tickets are priced at $27 each, but each additional block of 100 tickets purchased decreases the cost of each ticket by 50¢. How many blocks of tickets should be sold to maximize the revenue? (Round your answer to the nearest integer.) blocks Cust 27 x1 b-^/> (26.5D)+ ... +l» (27- 0.5 (e- Rox) lro (27+26.soT f2,05x)) 54.5-0.5) 5o(54. s fenenhahng Re with respect So(54.5-) ×ニ S45全 ssもldes 8. A rain gutter is formed by bending up the sides of a 30-inch-wide rectangular metal sheet. (a) Find a function A that models the cross-sectional area of the gutter in terms of x c30-2x) Crs ecsoml Aree 30-2 と A(x) 30x-2x (b) Find the value of x that maximizes the cross-sectional area of the gutter. tferenhan A) w.Y.. x, weak 30-4× ニ。 * 7.s n x = 7.s in (c) What is the maximum cross-sectional area for the gutter? Se.cch vea 7 3-2C7.s)) Ax)ophx= 1 12.5 in^2