Thread: Marginal Cost/Demand and Cost

1. The Marginal Cost of a product is modeled by dC/dx = 4/(x+1)^1/2
When x=15, C=50. Find the Cost function.

2. The demand and cost functions for a product are given by:
p=600 -3x
C=0.3x^2+6x+600
where p is the price per unit, x is the number of units, and C is the total cost. The profit for producing x units is given by:
P=xp - C -xt
where t is the excise tax per unit. Find the maximum profits for excise taxes of t=$5, $10, and $20.

Help for these two questions would be great! thanks

Originally Posted by Auger

1. The Marginal Cost of a product is modeled by dC/dx = 4/(x+1)^1/2
When x=15, C=50. Find the Cost function.

2. The demand and cost functions for a product are given by:
p=600 -3x
C=0.3x^2+6x+600
where p is the price per unit, x is the number of units, and C is the total cost. The profit for producing x units is given by:
P=xp - C -xt
where t is the excise tax per unit. Find the maximum profits for excise taxes of t=$5, $10, and $20.

Help for these two questions would be great! thanks

1) Integrate, use extra info to solve for the constant of integration.
2)Differentiate P and find critical points. Do this three times for t=5,10,20

Thanks. For #1, I did use integration by substitution, making u=x+1, i ended up getting I= 4ln(x+1)^1/2 + C. I sub'd in the c and x values, and got an answer of approx. 55.55, however the answer in the back of the book is C= 8(x+1)^1/2 + 18. What am I doing wrong?
For #2, I did just that, filling in equation P and finding the derivative, and i got the values: $5 ->-89.24, $10 -> -88.48, and $20 -> -86.97
I don't know if anyone is willing to see what they get, but my answers just seem off. Thanks

There won't be any natural logs in the answer. It's a simple power rule situation.

Thanks again but I still don't understand how they got the answer: 8(x+1)^1/2 + 18