Solution 1. The area A of the metal region = 76 cm2 2. Let x = width of the frame
x
xx(5 + 2x) 10 cm
5 cm x (10 + 2x)
3. Metal area A = area of frame – area of glass A = (10 + 2x)(5 + 2x) – 10 × 5 76 = 4 x 2 + 30x
EXAMPLE 21
The profi t P in euro per week of a local newspaper is g iven by P = – 0⋅0025 x 2 + 10 x – 6000, 0 ≤ x ≤ 2500, where x is the number of newspapers sold per week.
Find:
(a) the break-even point (the value of x for which there is no profi t),
(b) the number of newspapers that must be sold to give a profi t of €2400 per week.
Solution P = – 0⋅0025 x 2 + 10x – 6000
(a) Break-even point:
P = 0: – 0⋅0025x 2 + 10x – 6000 = 0 0⋅0025 x 2 – 10x + 6000 = 0 x =
__________________________ 2(0⋅0025)
10 ± √
_____________________ (–10 ) 2 – 4(0⋅0025)(6000)
∴ x = 3264·9, 735·09
Reject 3264·9 because it is not in the domain. Answer: 735 newspapers
(b) P = €2400: – 0⋅0025 x 2 + 10x – 6000 = 2400 – 0⋅0025 x 2 + 10x – 8400 = 0 0⋅0025 x 2 – 10x + 8400 = 0
