Page 235 - How To Solve Word Problems In Calculus

2
p(x) = (x + 2x) 2
dp dp dx
= ·
dt dx dt
dx
2
= 2(x + 2x)(2x + 2)
dt
The number of yachts produced in 6 months = 4 · 6 = 24
dp
2
When x = 24, = 2(24 + 48)(48 + 2)(4)
dt
= 2(624)(50)(4)
= 249,600 dollars per month

4. (a) R(x) = 300x + 0.075x 2 (b) R(51) = 300(51) + 0.075(51) 2
= 15,495.08

R (x) = 300 + 0.15x R(50) = 300(50) + 0.075(50) 2
= 15,187.50
R (50) = 300 + 0.15(50) R(51) − R(50) = $307.58

= $307.50

5. Let R(x), C (x), and P(x) represent the revenue, cost, and profit,
respectively, in producing x items.Then P (x) = R(x) − C (x)

R(x) = (price per unit sold)(number of units sold)

= (500 − 2x)x
= 500x − 2x 2

P (x) = R(x) − C (x)
2
= 500x − 2x − (50x + 400)
2
= 450x − 2x − 400
P (x) = 450 − 4x

P (99) = $54

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