Maximizing Things

[pepsissister]

1. Find the number of units that must be produced and sold in order to yield the maximum profit, given the following equations for revenue and cost:
R(x): 7x
C(x): .001x^2+.9x+20

2. A piece of molding 179 cm long is cut to form a rectangular picture frame. What dimensions will enclose the largest area?

3. A man 6ft tall walks at a rate of 2ft/s away from a lamppost that is 13 ft high. At which rate is the length of the shadow changing when he is 35 ft away from the lamppost?

4. A ladder is slipping down a vertical wall . If the ladder is 20ft long and the top of it is slipping at the constant rate of 2ft/s, how fast is the bottom of the ladder moving along the ground when the bottom is 16ft from the wall?

5. Given the revenue and cost functions R= 32x-.3x^2 and C= 5x+13, where x is the daily production, find the rate of change of profit with respect to time when 10 units are produced and the rate of change of production is 8 units per day.


TKHunny - Changed to more useful title.

 

[tkhunny]

R(x): 7x
C(x): .001x^2+.9x+20

You'll need a profit function. P(x) = R(x) - C(x). You should then recognize the quadratic function and track down that maximum.

You're going to have to start showing your work.