Chapter 8 linear appliCaTionS 235We begin by substituting numbers given in the problem for variables in the
formula.
(a) If 12,000 units are sold, then x = 12,000. The profit equation then
becomes P = 2(12,000) – 4000 = 24,000 – 4000 = 20,000. The profit is
$20,000.
(b) Think of a loss as a negative profit. When 1500 units are sold, P = 2x –
4000 becomes P = 2(1500) – 4000 = 3000 – 4000 = –1000. The manufac-
turer loses $1000 when 1500 units are sold.
(c) If the profit is $3000, then P = 3000; P = 2x – 4000 becomes 3000 =
2 x – 4000.
3000 2 4000
4000 4000
7000 2
7000
2
3500
=−
++
=
=
=xx
x
xA total of 3500 units were sold.
(d) The break-even point occurs when the profit is zero, that is when P = 0,
so P = 2x – 4000 becomes 0 = 2x – 4000.
02 4000
4000 4000
4000 2
4000
2
2000
=−
++
=
=
=xx
x
xThe manufacturer must sell 2000 units in order to break even.
A box has a square bottom. The height has not yet been determined, but
the bottom is 10” by 10”. The volume formula is V = lwh, because each of
the length and width is 10, lw becomes 10 · 10 = 100. The formula for the
box’s volume is V = 100h.
(a) If the height of the box is to be 6 inches, what is its volume?
(b) If the volume is to be 450 cubic inches, what should its height be?
(c) If the volume is to be 825 cubic inches, what should its height be?