Access over 20 million homework documents through the notebank

Get on-demand Q&A homework help from verified tutors

Read 1000s of rich book guides covering popular titles

Anonymous

Provide an appropriate response. 1)Let C(x) be the cost function and R(x) the revenue function. Compute the marginal cost, marginal revenue, and the marginal profit functions. C(x) = 0.0004x3 - 0.036x2 + 200x + 40,000 R(x) = 450x

1)

Solve the problem. 2)The demand equation for a certain item is p = 14 - x 1,000 and the cost equation is C(x) = 7,000 + 4x. Find the a) revenue function and b) marginal profit at a production level of 3,000 and interpret the result.

2)

Use the price-demand equation to determine whether demand is elastic, inelastic, or unitary at the indicated values of p. 3)x = f(p) = 276 - 4p; p = 48. 3)

4)How is revenue effected for the problem above (increase, decrease, stays the same)? Explain.

4)

1

Use the price-demand equation to find the values of p which meet the given condition of elasticity. 5)x = f(p) = 216-2p2; determine the values of p for which demand is elastic and the values of p for which demand is inelastic.. 5)

Solve the problem. 6)The annual revenue and cost functions for a manufacturer of zip drives are approximately R(x) = 520x - 0.02x2 and C(x) = 160x + 100,000, where x denotes the number of drives made. What is the maximum annual profit?

6)

7)A rectangular field is to be enclosed on four sides with a fence. Fencing costs $8 per foot for two opposite sides, and $4 per foot for the other two sides. Find the dimensions of the field of area 830 ft2 that would be the cheapest to enclose.

7)

Find where the following function is increaseing and decreasing. 8)f(x) = x3 - 4x 8)

2

Determine where the given function is concave up and where it is concave down. 9)q(x) = 9x3 + 2x + 5 9)

10)Graph the following equation and provide information on a) vertical asymptotes, b) horizontal asymptotes, c) intercepts, d) critical numbers,e) where the function is increasing/decreasing, f) inflection points, g) concavity, h) any min/max

10)

y = 6x x2 + 1

Repeat the directions from the problem above for the following equation. 11)y = 5x + 9 . 11)

Name___________________________________
Math 145-201
Exam #3
Provide an appropriate response.
1) Let C(x) be the cost function and R(x) the revenue function. Compute the marginal cost,
marginal revenue, and the marginal profit functions.
C(x) = 0.0004x3 - 0.036x2 + 200x + 40,000
1)
R(x) = 450x
Solve the problem.
2) The demand equation for a certain item is p = 14 -
x and the cost equation is C(x) =
1,000
2)
7,000 + 4x. Find the a) revenue function and b) marginal profit at a production level of
3,000 and interpret the result.
Use the price-demand equation to determine whether demand is elastic, inelastic, or unitary at the indicated values of
p.
3) x = f(p) = 276 - 4p; p = 48.
3)
4) How is revenue effected for the problem above (increase, decrease, stays the same)?
Explain.
1
4)
Use the price-demand equation to find the values of p which meet the given condition of elasticity.
5) x = f(p) = 216-2p2; determine the values of p for which demand is elastic and the values
5)
of p for which demand is inelastic..
Solve the problem.
6) The annual revenue and cost functions for a manufacturer of zip drives are
approximately R(x) = 520x - 0.02x2 and C(x) = 160x + 100,000, where x denotes the
6)
number of drives made. What is the maximum annual profit?
7) A rectangular field is to be enclosed on four sides with a fence. Fencing costs $8 per foot
for two opposite sides, and $4 per foot for the other two sides. Find the dimensions of
the field of area 830 ft2 that would be the cheapest to enclose.
Find where the following function is increaseing and decreasing.
8) f(x) = x 3 - 4x
2
7)
8)
Determine where the given function is concave up and where it is concave down.
9) q(x) = 9x3 + 2x + 5
10) Graph the following equation and provide information on a) vertical asymptotes, b)
horizontal asymptotes, c) intercepts, d) critical numbers,e) where the function is
increasing/decreasing, f) inflection points, g) concavity, h) any min/max
y=
9)
10)
6x
x2 + 1
Repeat the directions from the problem above for the following equation.
11) y =
5x + 9 .
11)
3
Name___________________________________
Math 145
Practice Problems- Marginal Analysis & Elasticity of Demand
Provide an appropriate response.
1) Suppose that the total profit in hundreds of dollars from selling x items is given by P(x) =4x2 5x + 10. Find the marginal profit at x = 5.
A) $35
B) $45
C) $15
D) $32
1)
Solve the problem.
2) The demand equation for a certain item is p = 14 -
x and the cost equation is C(x) = 7,000 +
1,000
2)
4x. Find the marginal profit at a production level of 3,000 and interpret the result.
A) $14; at the 3,000 level of production, profit will increase by approximately $14 for each
unit increase in production.
B) $7; at the 3,000 level of production, profit will increase by approximately $7 for each unit
increase in production.
C) $16; at the 3,000 level of production, profit will increase by approximately $16 for each
unit increase in production.
D) $4; at the 3,000 level of production, profit will increase by approximately $4 for each unit
increase in production.
Find the elasticity of the demand function as a function of p.
3) x = D(p) = 700 - p
p
1
A) E(p) =
B) E(p) =
2p - 1400
1400 - 2p
C) E(p) =
p
700 - p
D) E(p) =
3)
p
1400 - 2p
Use the price-demand equation to determine whether demand is elastic, is inelastic, or has unit elasticity at the
indicated values of p.
4) x = f(p) = 2005 - p2; p = 13
4)
A) Elastic
B) Inelastic
C) Unit elasticity
Use the price-demand equation to find the values of p which meet the given condition of elasticity.
5) x = f(p)= 246 - 8p; determine the values of p for which demand has unit elasticity. Round to two
decimal places if necessary.
A) Inelastic at p = 31.36
B) Inelastic at p = 15.38
C) Inelastic at p = 15.68
D) Inelastic at p = 7.69
1
5)
Answer Key
Testname: PRACTICE PROBLEMS- MARGINAL ANALYSIS & ELASTICITY OF DEMAND
1) A
2) D
3) D
4) B
5) B
2
Name___________________________________
Math 145
Practice Problems- Optimization
Solve the problem.
1) A rectangular field is to be enclosed on four sides with a fence. Fencing costs $8 per foot for two
opposite sides, and $4 per foot for the other two sides. Find the dimensions of the field of area
830 ft2 that would be the cheapest to enclose.
A) 57.6 ft @ $8 by 14.4 ft @ $4
C) 40.7 ft @ $8 by 20.4 ft @ $4
1)
B) 20.4 ft @ $8 by 40.7 ft @ $4
D) 14.4 ft @ $8 by 57.6 ft @ $4
2) Find the dimensions that produce the maximum floor area for a one-story house that is
rectangular in shape and has a perimeter of 139 ft.
A) 34.75 ft × 139 ft
B) 11.58 ft × 34.75 ft
C) 34.75 ft × 34.75 ft
D) 69.5 ft × 69.5 ft
2)
3) From a thin piece of cardboard 10 in. by 10 in., square corners are cut out so that the sides can be
folded up to make a box. What dimensions will yield a box of maximum volume? What is the
maximum volume? Round to the nearest tenth, if necessary.
A) 5 in. by 5 in. by 2.5 in.; 62.5 in.3
B) 3.3 in. by 3.3 in. by 3.3 in.; 37 in.3
3)
C) 6.7 in. by 6.7 in. by 3.3 in.; 148.1 in.3
D) 6.7 in. by 6.7 in. by 1.7 in.; 74.1 in.3
1
Answer Key
Testname: PRACTICE PROBLEMS- OPTIMIZATION
1) B
2) C
3) D
2
...

Student has agreed that all tutoring, explanations, and answers provided by the tutor will be used to help in the learning process and in accordance with Studypool's honor code & terms of service.

This question has not been answered.

Create a free account to get help with this and any other question!

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors