Chapter 11 Additional Topics
Chapter 11 Additional Topics
Chapter 11 Additional Topics
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SSM: Intermediate Algebra Homework <strong>11</strong>.5<br />
7. x = dollars invested in CD<br />
y = dollars invested in mutual fund<br />
a. x + y = 6000 or y = 6000 - x<br />
I = .0285 x + .09y<br />
f ( x) = .0285 x + .09(6000 − x)<br />
= .0285 x + .09⋅6000 − .09x<br />
f ( x) = − .0615x + 540 0≤ x ≤6000<br />
b. We evaluate f (0) = $540. Thus the I-<br />
intercept is (0, 540). This means that if the<br />
entire $6000 is invested in the mutual fund,<br />
$540 in interest will be earned. Since f is a<br />
decreasing function, $540 is also the<br />
maximum interest that can be earned.<br />
c. The x-intercept occurs when f (x) = 0.<br />
So<br />
− .0615x<br />
+ 540 = 0<br />
− .0615x<br />
= − 540<br />
−540<br />
x = = $8780.49<br />
−.0615<br />
Thus the x-intercept is (8780.49, 0).<br />
Although the formula for f ( x)<br />
yields a<br />
plausible result for f (x) = 0 , this value is<br />
outside the domain of f , since only $6000 is<br />
available for investment. It is also illogical<br />
to invest a large sum of money that returns<br />
no interest. Thus model breakdown has<br />
occurred.<br />
d. The slope of f is − 0.0615 . It means that<br />
for every additional dollar invested in the<br />
CD, 6.15 cents less interest is received.<br />
b. f is decreasing. The more $50 tickets sold,<br />
the less revenue will be earned.<br />
c. f (16000) = − 25(16000) + 1500000<br />
= 1,100,000.<br />
If 16000 of the $50 tickets are sold and 4000<br />
of the $75 tickets are sold, the total revenue<br />
will be $1,100,000.<br />
d. We want R = cost + profit = $1,075,000.<br />
− 25x<br />
+ 1500000 = 1075000.<br />
− 25x<br />
= − 425000.<br />
−425000<br />
x = = 17000<br />
−25<br />
Thus we should sell 17000 of the $50 tickets<br />
and 3000 of the $75 tickets to make<br />
$600,000 profit.<br />
<strong>11</strong>. x = number of $45 tickets sold<br />
y = number of $70 tickets sold<br />
a. x + y = 12000 or y = 12000 − x<br />
b.<br />
R = 45x + 70y<br />
f ( x) = 45x + 70(12000 − x)<br />
= 45x<br />
+ 70⋅12000 − 70x<br />
f ( x) = − 25x + 840000 0≤ x ≤12000<br />
9. x = number of $50 tickets sold<br />
y = number of $75 tickets sold<br />
a. x + y = 20000 or y = 20000 − x<br />
R = 50x + 75y<br />
f ( x) = 50x + 75(20000 − x)<br />
= 50x<br />
+ 75⋅ 20000 − 75x<br />
f ( x) = − 25x + 1500000 0≤ x ≤ 20000<br />
c. Since f is a decreasing function and<br />
0 ≤ x ≤ 12000 , the minimum revenue<br />
possible will be<br />
f (12000) = − 25(12000) + 840000 = 540,000<br />
and the maximum revenue possible will be<br />
f (0) = − 25(0) + 840000 = 840,000.<br />
Thus the earned revenue will be between<br />
$540,000 and $840,000.<br />
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