Page 39 - How To Solve Word Problems In Calculus

9. Let x represent the number of trees to be planted in excess of 500.
Let N(x) represent the number of apples as a function of x. The
total number of trees is then 500 + x and each tree will produce
800 − 20x apples.
Total number of apples
= (number of apples produced by each tree)(number of trees)

N(x) = (800 − 20x)(500 + x)
= 400,000 − 9200x − 20x 2

10. Let x represent the number of computers sold. The cost of
producing x computers is the sum of the fixed cost and the variable
cost.

C = 2000 + 800x

Fixed cost Cost to make
x computers
If 10 or fewer computers are sold, the price is $1500 per computer, so
the company’s revenue R = 1500x. The profit,

P = R − C
= 1500x − (2000 + 800x)

= 700x − 2000
If more than 10 computers are sold, the number of computers in
excess of 10 is x − 10. The price per computer then becomes
1500 − 10(x − 10) = 1600 − 10x dollars. In this case the
company’s revenue becomes R = (1600 − 10x)x = 1600x − 10x 2
and the profit
P = R − C
2
= 1600x − 10x − (2000 + 800x)
2
= 800x − 10x − 2000
Combining these results,
700x − 2000 if x ≤ 10

P (x) = 2
800x − 10x − 2000 if x > 10

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