Page 30 - How To Solve Word Problems In Calculus

cost, and profit in producing x clay figures as a function of
time.

Solution
Step1
Let x represent the number of clay figures produced
and let t represent the number of hours needed to produce
them. Let R, C, and P represent the revenue, cost, and profit,
respectively.

Step2
Since each figure sells for $10,

R = 10x

The cost consists of three parts. Fixed cost is $750, the cost of
running the machine for t hours is 6t dollars, and the cost of
material to produce x figures is 2x dollars. Thus

C = 750 + 6t + 2x

Since Profit = Revenue − Cost

P = R − C

= 10x − (750 + 6t + 2x)
= 8x − 6t − 750

Step3
Since 12 clay figures are produced per hour, x = 12t.
Substituting into the results of step 2,

R = 10x = 10(12t)
R(t) = 120t

C = 750 + 6t + 2x
= 750 + 6t + 2(12t)

= 750 + 6t + 24t

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