11 A calculator manufacturer has the total cost function Cx

11. A calculator manufacturer has the total cost function C(x) = 34x + 6484 and the total revenue function R(x) = 61x.

(a) What is the equation of the profit function P(x) for the calculator?
P(x) =  

(b) What is the profit on 2200 units?
P(2200) = $

12. A manufacturer of DVD players has monthly fixed costs of $9800 and variable costs of $50 per unit for one particular model. The company sells this model to dealers for $95 each.

(a) For this model DVD player, write the function for monthly total costs.
C(x) =  

(b) Write the function for total revenue.
R(x) =  

(c) Write the function for profit.
P(x) =  

(d) Find C(210), R(210), and P(210).

(e) Find C(350), R(350), and P(350).

(f) Find the marginal profit.
$

13. A jewelry maker incurs costs for a necklace according to the equation shown below.

C(x) = 36x + 1650

The revenue function for the necklaces is given below.

R(x) = 86x

How many necklaces must be sold to break even?

14. Find the market equilibrium point for the following demand and supply functions.

Demand:        p = -2q + 288

Supply:          p = 8q + 5

p = $

15. Solve the equation by using the quadratic formula. (Enter your answers as a comma-separated list.)

x² 4x 4 = 0

(a) Give exact real answers.
x =  
(b) Give answers rounded to two decimal places.
x =

16. Use any method to find the exact real solution, if it exists. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)

4 = 0

17. Solve using quadratic methods. (Enter your answers as a comma-separated list.)

(x + 5)² + 5(x + 5) + 4 = 0

x =

18. Consider the following equation.

y = (-1/22)x^2 + x

(a) Find the vertex of the graph of the equation.

(x , y) = (  )
(b) Determine if the vertex is a maximum or minimum point.

maximum minimum    

(c) Determine what value of x gives the optimal value of the function.
x =  

(d) Determine the optimal (maximum or minimum) value of the function.
y =

19. Consider the following equation.

x² + x + 6y = 8

Determine whether the function\'s vertex is a maximum point or a minimum point.

Find the coordinates of this point.
(x, y) = (  )

Find the zeros. (Enter your answers as a comma-separated list.)
x =

20. The daily profit from the sale of a product is given by P = 14x 0.1x² 50 dollars, where x is the number of units of production.

(a) What level of production maximizes profit?


(b) What is the maximum possible profit?
$

C(210)	=	$
R(210)	=	$
P(210)	=	$

Solution

11) P(X)=R(x)-c(x) a) P(X) =27x-6484 B) p(2200) 52916 DOLLARS C) c(X) 50X+9800 B) R(x) 95x C) P(x) 45x-9800 d) C(210) 20300 R(210) 19950 P(210) -350 f ) Marginal profit P\'(x) 45 13) C=R gives 36x+1650 = 86x x 33 Break even units = 33 14) p = -2q+288     p=8q+5 Equate the two 10q = 283 Equilibrium units =28.3 or 28 units