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WebAssign
131-lab#5(1.6&2.1) (Homework)
Current Score : – / 31
Sarah Saad
MTH131, section 02, Fall 2017
Instructor: Maila Brucal-Hallare
Due : Sunday, November 12 2017 11:59 PM EST
1. –/2 pointsHarMathAp11 1.6.001.MI.
Suppose a calculator manufacturer has the total cost function C(x) = 22x + 6600 and the total revenue
function R(x) = 64x.
(a) What is the equation of the profit function P(x) for the calculator?
P(x) =
(b) What is the profit on 2400 units?
P(2400) = $
2. –/3 pointsHarMathAp11 1.6.005.
A linear cost function is C(x) = 9x + 100. (Assume C is measured in dollars.)
(a) What are the slope and the C-intercept?
slope
C-intercept
(b) What is the marginal cost MC ?
MC =
What does the marginal cost mean?
If production is increased by this many units, the cost decreases by $1.
Each additional unit produced reduces the cost by this much (in dollars).
If production is increased by this many units, the cost increases by $1.
Each additional unit produced costs this much (in dollars).
(c) How are your answers to parts (a) and (b) related?
slope = fixed costs, and C-intercept = marginal cost
slope
= marginal cost
C-intercept
slope = marginal cost, and C-intercept = fixed costs
C-intercept
= marginal cost
slope
(d) What is the cost of producing one more item if 50 are currently being produced?
$
What is the cost of producing one more item if 100 are currently being produced?
$
3. –/4 pointsHarMathAp11 1.6.011.MI.SA.
This question has several parts that must be completed sequentially. If you skip a part of the question, you
will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Tutorial Exercise
A company charting its profits notices that the relationship between the number of units sold, x, and the profit,
P, is linear. If 200 units sold results in $2700 profit and 250 units sold results in $5500 profit, write the profit
function for this company. Find the marginal profit.
4. –/5 pointsHarMathAp11 1.6.013.
Extreme Protection, Inc. manufactures helmets for skiing and snowboarding. The fixed costs for one model of
helmet are $6300 per month. Materials and labor for each helmet of this model are $40, and the company
sells this helmet to dealers for $70 each. (Let x represent the number of helmets sold. Let C, R, and P be
measured in dollars.)
(a) For this helmet, write the function for monthly total costs C(x).
C(x) =
(b) Write the function for total revenue R(x).
R(x) =
(c) Write the function for profit P(x).
P(x) =
(d) Find C(200).
C(200) =
Interpret C(200).
When this many helmets are produced the cost is $200.
For each $1 increase in cost this many more helmets can be produced.
This is the cost (in dollars) of producing 200 helmets.
For every additional helmet produced the cost increases by this much.
Find R(200).
R(200) =
Interpret R(200).
When this many helmets are produced the revenue generated is $200.
This is the revenue (in dollars) generated from the sale of 200 helmets.
For each $1 increase in revenue this many more helmets can be produced.
For every additional helmet produced the revenue generated increases by this much.
Find P(200).
P(200) =
Interpret P(200).
This is the profit (in dollars) when 200 helmets are sold, but since it is negative it means that
the company loses money when 200 helmets are sold.
For each additional helmet sold the profit (in dollars) increases by this much, but since it is
negative it means that the company needs to decrease the number of helmets sold in order to
make a profit.
This is the profit (in dollars) when 200 helmets are sold, and since it is positive it means that the
company makes money when 200 helmets are sold.
For each additional helmet sold the profit (in dollars) increases by this much, but since it is
positive it means that the company is producing too many helmets.
(e) Find C(300).
C(300) =
Interpret C(300).
For every additional helmet produced the cost increases by this much.
This is the cost (in dollars) of producing 300 helmets.
For each $1 increase in cost this many more helmets can be produced.
When this many helmets are produced the cost is $300.
Find R(300).
R(300) =
Interpret R(300).
This is the revenue (in dollars) generated from the sale of 300 helmets.
For each $1 increase in revenue this many more helmets can be produced.
When this many helmets are produced the revenue generated is $300.
For every additional helmet produced the revenue generated increases by this much.
Find P(300).
P(300) =
Interpret P(300).
This is the profit (in dollars) when 300 helmets are sold, and since it is positive it means that the
company makes money when 300 helmets are sold.
For each additional helmet sold the profit (in dollars) increases by this much, but since it is
positive it means that the company is producing too many helmets.
This is the profit (in dollars) when 300 helmets are sold, but since it is negative it means that
the company loses money when 300 helmets are sold.
For each additional helmet sold the profit (in dollars) increases by this much, but since it is
negative it means that the company needs to decrease the number of helmets sold in order to
make a profit.
(f) Find the marginal profit MP.
MP =
Write a sentence that explains its meaning.
For each $1 increase in profit this many more helmets can be produced.
When costs are decreased by this much the profit is increased by $1.
When revenue is increased by this much the profit is increased by $1.
Each additional helmet sold increases the profit by this many dollars.
5. –/3 pointsHarMathAp11 1.6.019.
A manufacturer sells belts for $12 per unit. The fixed costs are $2000 per month, and the variable cost per
unit is $8.
(a) Write the equations of the revenue R(x) and cost C(x) functions.
R(x) =
C(x) =
(b) Find the break-even point.
It takes
units to break even.
6. –/3 pointsHarMathAp11 1.6.031.
The graphs of the demand function and supply function for a certain product, are given below. Use these
graphs to answer the questions.
(a) How many units q are demanded when the price p is $50?
q=
(b) How many units q are supplied when the price p is $50?
q=
(c) Will there be a market surplus (more supplied) or shortage (more demanded) when p = $50?
surplus
shortage
7. –/5 pointsHarMathAp11 1.6.039.
Complete the problem by using the accompanying figure, which shows a supply function and a demand
function. (Assume price is measured in dollars.)
(a) Label each function as “demand” or “supply.”
function 1
—Select—
function 2
—Select—
(b) Which of the labeled points is the equilibrium point?
point A
point B
point C
point D
Determine the price and quantity at which market equilibrium occurs.
price
quantity
$
units
8. –/1 pointsHarMathAp11 1.6.044.MI.
Find the market equilibrium point for the following demand and supply functions.
Demand:
Supply:
p = −2q + 286
p = 8q + 4
(q, p) =
9. –/1 pointsHarMathAp11 2.1.005.
Solve the equation by factoring. (Enter your answers as a comma-separated list.)
x2 − 4x = 12
x=
10.–/2 pointsHarMathAp11 2.1.013.MI.
Solve the equation by using the quadratic formula. (Enter your answers as a comma-separated list. If there is
no real solution, enter NO REAL SOLUTION.)
x2 − 6x = 9
(a) Give real answers exactly.
x=
(b) Give real answers rounded to two decimal places.
x=
11.–/1 pointsHarMathAp11 2.1.039.MI.
Multiply both sides of the equation by the LCD and solve the resulting quadratic equation. (Enter your answers
as a comma-separated list.)
x+
x=
2
=3
x
12.–/1 pointsHarMathAp11 2.1.045.MI.
If the profit from the sale of x units of a product is P = 95x − 200 − x2, what level(s) of production will yield
a profit of $1000? (Enter your answers as a comma-separated list.)
x=
units
WebAssign
131-lab#6 (2.2-2.4&4.1) (Homework)
Current Score : – / 39
Sarah Saad
MTH131, section 02, Fall 2017
Instructor: Maila Brucal-Hallare
Due : Sunday, November 12 2017 11:59 PM EST
1. –/4 pointsHarMathAp11 2.2.003.
Consider the following equation.
y = 6 + 6x − x2
(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=
2. –/5 pointsHarMathAp11 2.2.007.MI.
Determine whether the function’s vertex is a maximum point or a minimum point.
1 2
x
4
The vertex is a maximum point.
y=x−
The vertex is a minimum point.
Find the coordinates of this point.
(x, y) =
Find the zeros, if any exist. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
x=
Find the y-intercept.
y=
Sketch the graph of the function.
3. –/5 pointsHarMathAp11 2.2.009.
Determine whether the function’s vertex is a maximum point or a minimum point.
y = x2 + 4x + 4
The vertex is a maximum point.
The vertex is a minimum point.
Find the coordinates of this point.
(x, y) =
Find the zeros, if any exist. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
x=
Find the y-intercept.
y=
Sketch the graph of the function.
4. –/2 pointsHarMathAp11 2.2.013.
Consider the following.
y = (x − 6)2 + 1
(a) Tell how the graph of y = x2 is shifted.
The graph is shifted 6 units to the right and 1 unit down.
The graph is shifted 6 units to the left and 1 unit up.
The graph is shifted 1 unit to the right and 6 units down.
The graph is shifted 1 unit to the left and 6 units up.
The graph is shifted 6 units to the right and 1 unit up.
(b) Graph the function.
5. –/2 pointsHarMathAp11 2.2.031.
The daily profit from the sale of a product is given by P = 18x − 0.1×2 − 150 dollars.
(a) What level of production maximizes profit?
units
(b) What is the maximum possible profit?
$
6. –/1 pointsHarMathAp11 2.3.001.
The total costs for a company are given by
C(x) = 1200 + 60x + x2
and the total revenues are given by
R(x) = 140x.
Find the break-even points. (Enter your answers as a comma-separated list.)
x=
units
7. –/1 pointsHarMathAp11 2.3.009.
If, in a monopoly market, the demand for a product is p = 105 − 0.80x and the revenue function is R = px, where x is the number of
units sold, what price will maximize revenue?
$
8. –/2 pointsHarMathAp11 2.3.025.
If the supply function for a commodity is p = q2 + 4q + 16 and the demand function is p = −2q2 + 5q + 436, find the equilibrium
quantity and equilibrium price.
equilibrium quantity
equilibrium price
$
9. –/2 pointsHarMathAp11 2.4.013.
Decide whether each function whose graph is shown is the graph of a cubic (third-degree) or quartic (fourth-degree) function.
(a)
cubic
quartic
(b)
cubic
quartic
10.–/1 pointsHarMathAp11 2.4.023.
Graph the function.
y = (x + 1)(x − 2)(x − 1)
11.–/4 pointsHarMathAp11 2.4.033.
If k(x) =
1
x+2
1−x
if x < 0 if 0 ≤ x < 1 , find the following. if x ≥ 1 (a) k(−7) (b) k(0) (c) k(1) (d) k(−0.001) 12.–/4 pointsHarMathAp11 2.4.037. Consider the following. f(x) = 2x + 4 x+4 (a) Graph the function with a graphing utility. (b) Classify the function as a polynomial function, a rational function, or a piecewise defined function. polynomial function rational function piecewise defined function (c) Identify any asymptotes. (Enter your answers as a comma-separated list of equations. If an answer does not exist, enter DNE.) (d) Use the graph to locate turning points. (Enter your answers as a comma-separated list. Round your answers to one decimal place. If an answer does not exist, enter DNE.) x= 13.–/3 pointsHarMathAp11 2.4.047. If 160 feet of fence is to be used to enclose a rectangular yard, then the resulting area of the fenced yard is given by A = x(80 − x) where x is the width of the rectangle. (a) If A = A(x), find A(3) and A(20). A(3) = ft2 A(20) = ft2 (b) What restrictions must be placed on x (the domain) so that the problem makes physical sense? (Enter your answer using interval notation.) 14.–/1 pointsHarMathAp11 4.1.001.MI. Graph the inequality. y ≤ 4x − 2 15.–/1 pointsHarMathAp11 4.1.003. Graph the inequality. x y + <1 4 3 16.–/1 pointsHarMathAp11 4.1.005. Graph the inequality. 0.2x ≥ 1.6 ... Purchase answer to see full attachment

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