Answer:
Step-by-step explanation:
y = ax² + bx + c
~~~~~~~
(4, - 2), (8, 6), (2, 0)
a(4²) + b(4) + c = - 2
a(8²) + b(8) + c = 6
a(2²) + b(2) + c = 0
16a + 4b + c = - 2 .............. <em>(1)</em>
64a + 8b + c = 6 ............... <em>(2)</em>
4a + 2b + c = 0 ................. <em>(3)</em>
a = 0.5 ; b = - 4 ; c = 6
<em>y = 0.5x² - 4x + 6</em>
Part A: (0, 6), (6, 0)
Part B: (0,6)
Part C: (6, 0)
Part D: [ 4, ∞ )
Answer:
(a) P(x) = 300 x - 3600
(b) P(340) = $ 98400
(c) At least 12 items must be sold to avoid losing money.
Step-by-step explanation:
Part (a):
The Profit function is the difference between the revenue function (R(x)) and the Cost (C(x)) function:
P(x) = R(x) - C(x)
P(x) = 384 x - [84 x + 3600]
P(x) = 384 x - 84 x - 3600
P(x) = 300 x - 3600
Part (b):
The profit on 340 items is:
P(340) = 300 (340) - 3600
P(340) = 102000 - 3600
P(340) = $ 98400
Part (c):
To avoid losing money, the profit P(x) has to be larger or equal than zero. That is:
P(x) 0
300 x -3600 0
300 x 3600
x 3600/300
x 12
So at least 12 items must be sold to avoid losing money.