Nobody downloaded yet

Exercises - Math Problem Example

Comments (0) Cite this document
Summary
The paper "Math Exercises" is purposed to give answers and explanations on assignment on Math. The answers on questions are full and clear and include full solutions. The test is purposed to summarize the knowledge, to check the students' progress and to identify problem areas in studying…
Download full paperFile format: .doc, available for editing
GRAB THE BEST PAPER96.8% of users find it useful
Math Exercises
Read TextPreview

Extract of sample "Exercises"

Download file to see previous pages 1 A firm manufactures and sells q units of a product at price = £(575 – ½ q)
which has unit costs of £(q2 – 25q) and fixed costs of £45,000.

(a) Write down expressions for: revenue, profit and average cost
in terms of output(q) of the firm. [1 mark]

Revenue = (575 – ½ q ) q
= 575q – ½ q2

Profit = Revenue – Total Cost

= 575q – ½ q2 - [(q2 – 25q )q +45,000]

= 575q – ½ q2 – q3 + 25q2 - 45,000

= – q3 + 24.5q2 + 575q - 45,000

Average Cost = Total Cost / q

= q2 – 25q + 45,000/q


(b) Find expressions for: marginal revenue, marginal cost, marginal
profit and marginal average costs in terms of output (q). [2 marks]


Marginal Revenue, Marginal Cost, Marginal Profit and Marginal Average Costs is the derivative of Revenue, Cost, Profit, Average Costs . Since the derivative of f(x) = xn is nxn-1, we have:

Marginal Revenue = 575 – q

Marginal Cost = 3q2 -50q

Marginal Profit = -3q2 + 49q +575

Marginal Average Cost = 2q – 25 -45,000/q2 (since 1/q = q-1)

(c) Find the output levels of the firm that and confirm that the output levels found do indeed maximise or minimise these functions [ 1 mark]


(i) Maximise revenue

















• This is the graph of Revenue = 575q – ½ q2 , we can see that it is maximised at q = 575.


(ii) Minimise costs

To minimise costs, set marginal costs to 0

q = 50 / 3 or approx 17 units

















This is the graph of Costs = q3 - 25q2 + 45,000. We can see that the minimise value is approximately at q =17.


(iii) Maximise profits

To maximise profits, set marginal profits to 0

-3q2 + 49q +575 = 0

Using the quadratic formula, we have:

q = 23.23 , -7.89

Disregarding the negative value, we have:

q = 23 units.















This is the graph of Profit = -q3 + 24.5q2 + 575q - 45,000. We can see that the maximum value is approximately at q=23.


(iv) Minimise average costs

To minimise average costs, set marginal average costs to 0:


2q - 25 -45,000/q2 = 0 (multiply both sides by q2)

2q3 - 25q2 - 45,000 = 0

With the use of trial and error, we get the only possible value as:

q = 33 units.







This is the graph of Average Cost = q2 - 25q + 45,000/q. We can see that the maximum value is approximately at q=33.


2. The demand function for a product is given by the following expression:

q = 25 + 200
(p - 2)

(a) Calculate the demand at prices 3 and 7 [1/2 mark ]

For p = 3:

q = 25 + 200
(3 - 2)
q = 25 + 200

q = 225

For p = 7:

q = 25 + 200
(7 - 2)
q = 25 + 40

q = 65


Answer in (Q,P) form: (225,3), (65,7)


(b) Calculate the ARC elasticity of demand with respect to price
between the prices given in part (a) and comment on whether
demand is elastic or inelastic between these prices. [1/2 mark]

Earc = (Q2-Q1) / [(Q2+Q1)/2]
(P2-P1) / [(P2+P1)/2]

Earc = (65-225) / [(65+225)/2]
(7-3) / [(7+3)/2]

Earc = -160 / 145
4 / 5

Earc = -40 = -1.38
29

Since an "elastic" good is where price elasticity of demand is greater than one, we can consider that the demand is elastic between these prices.

(c) Find an expression for POINT elasticity of demand with respect
to price in terms of price. [ 1 mark]

Ept = (q/ p) * p/q

The derivative of q = 25 +200/(p-2) is

q/ p = 0 + -1 (200) (p-2)-2

And q = 25 +200/(p-2)

Hence:

Ept = [-200p/ (p-2)2]/ [25 +200/(p-2)]



(d) Calculate POINT elasticity of demand at prices 3 and 7 and
comment on their values and on the relationship between
ARC and POINT elasticity [1/2 mark]
Ept = [-200p/ (p-2)2]/ [25 +200/(p-2)]

Ept (3) = (-600/ 1)/ 225

= -2.67

Ept (7) = -56/ 65

= -0.862

The value of arc elasticity is in between the value of point elasticity which is expected ...Download file to see next pagesRead More
Cite this document
  • APA
  • MLA
  • CHICAGO
(“Math Exercises Problem Example | Topics and Well Written Essays - 1000 words”, n.d.)
Math Exercises Problem Example | Topics and Well Written Essays - 1000 words. Retrieved from https://studentshare.org/education/1513790-math-exercises
(Math Exercises Problem Example | Topics and Well Written Essays - 1000 Words)
Math Exercises Problem Example | Topics and Well Written Essays - 1000 Words. https://studentshare.org/education/1513790-math-exercises.
“Math Exercises Problem Example | Topics and Well Written Essays - 1000 Words”, n.d. https://studentshare.org/education/1513790-math-exercises.
  • Cited: 0 times
Comments (0)
Click to create a comment or rate a document

CHECK THESE SAMPLES OF Math Exercises

College Math Math Problem

...Math Problem a) I constructed the first linear function based on the municipal solid waste data for 1970 and 1997 and the second linear function based on the data for 1980 and 1997. A dependent variable is the annual production of municipal solid waste in million tons. An independent variable is the number of years after 1960. Based on the municipal solid waste data from the graph, I received such numbers for independent and dependent variables for the models. Model 1 Model 2 Dependent Variable Independent Variable Dependent Variable Independent Variable 121 10 152 20 217 37 217 37 Model 1: 121 = a + b*10 217 = a + b*37 The solution is a=85.4, b=3.56. Therefore, the first linear function is: Annual MSW =...
2 Pages(500 words)Math Problem

Exercises 4

...Running head: FINANCIAL ANALYSIS EXERCISES AND QUESTIONS Financial Analysis Questions and Exercises of Institution] Discussion Questions 9-11 CVP analysis is used to calculate the volume of units to be produced or services rendered in order to make a desired level of profit. This is a basic management tool which is frequently used in basic planning. In CVP analysis, the term breakeven means no-profit no-loss gain i.e that volume of products/services that will generate just enough income to cover fixed and variable costs. Discussion Questions 9-17 Direct costs are easily and physically traceable to a product or other unit of business or segment, while indirect cost are usually incurred to facilitate...
2 Pages(500 words)Essay

Math

...Derivatives of sine functions Investigate the derivative of the function Figure Graph of function and for Figure shows the graph of function (red curve) and it derivative (gradient) (green curve). From graph it can be seen that the gradient of the function behaves similarly as original function, however it shifts left side by (or shift right side by). = or From above, it is obvious that the graphs of the sine and it derivative cosine functions are sinusoids of different phases1. The derivative is also a sine function with a phase-shift of (or). Conjecture: The graphs of the sine function, and its derivative cosine function, are sinusoids of different phases i.e. the derivative is also a sine function with a phase-shift... of sine...
4 Pages(1000 words)Essay

Chemistry exercises

...CHEMISTRY the following compounds:  a) SiF4: Silicon tetrafluoride b) CaF2: Calcium fluoride c) NH4CI: Ammonium chloride d) (NH4)3(P04 Ammonium phospate e) PCL5: Phosphorous pentachloride f) H2S04: Sulphuric acid  2) For the reaction: 2AgN03 + BaCl2 ► 2AgCl + Ba(N03)2  If a solution containing 41.6g of AgN03 is mixed with a solution that contains 35.4g BaCl2:  a) which reagent is limiting and which in excess? Ans. 2AgN03 + BaCl2 ► 2AgCl + Ba(N03)2 The molar ratio between AgNO3 and BaCl2 is 2:1 Mr of AgNO3 = 169.87 Mr of BaCl2 = 208.33 Given mass of AgNO3= 41.6g Given mass of BaCl2= 35.4 g Moles = Mass/ Mr Moles of AgNO3 present in given mass= 41.6/169.87= 0.24489 moles Moles of BaCl2 present in given mass= 35.4/208.33= 0.1699 1... the...
11 Pages(2750 words)Essay

Math

...Death Penalty Thesis ment: The statistics used in death penalty cases can be used to argue for or against the practice, but rarely are all of the real statistics given. Outline I. Introduction II. Pro Death Penalty Statistics a. Victims b. Death Row Inmates with Prior Convictions III. Anti Death Penalty Statistics a. Race b. Education Level of Death Row Inmates IV. Real Death Penalty Statistics a. Race b. Number of Executions since 1930 V. Conclusion The statistics used in death penalty cases can be used to argue for or against the practice, but rarely are all of the real statistics given. Pro death penalty advocates generally state crime statistics, while anti death penalty advocates cite the cost... Penalty Thesis ment: ...
5 Pages(1250 words)Essay

Math

... XXXXX Number: XXXXX XXXXX XXXXXX XXXXX of XXXXX XX – Jun - 2010 Mathematics - Assignment A. What kind of correlation do you expect to find between annual income and amount spent on car? Will it be positive or negative? Will it be a strong relationship? Base your answer on your personal guess as well as by looking through the data. The two variables, annual income and amount spent on car are expected to have a positive correlation. The main reason is that when the income is higher, people tend to spend more on their cars. Moreover, the relationship between the two variables is expected to be strong. Based on the data given, it is evident that the annual income and the amount spent on car are directly proportional to one... XXXXX Number:...
4 Pages(1000 words)Essay

Exercises

...When and where do you plan your day? I plan my day immediately after the leave each day. I have the success and setbacks of the day still fresh in my mind at this point. I can see clearly what must be done and what plans need to be altered. I usually take fifteen minutes to do this. I put notes up on the board for the following day at this time and block out questions and objectives for the lesson that is to be taught the following day. When and where do you do lesson planning? Lesson planning is done is a block of time during the day. I have a planning period and I use it for this purpose. I close my door and turn off the classroom lights. This gives the appearance that I am not in my room. I love my colleagues... and where do you...
2 Pages(500 words)Research Paper

Writting exercises

... Writing exercises The production of films and photography is directed to different viewers all of which have various tastes and preferences. The different genres in epic productions are meant to characterize the viewers each with their favorites and opinion. All in all, these films are watched and the viewers present their various views on the cinematography, camera projections, feeling portrayed and induced, color features, acting and actors as a whole. It was discovered that movies whose main actors and most of the cast were feminine were highly watched by the male gender. Perhaps this is a new way of saying that like poles attract but indeed, the male gender has a habit of concentrating more on movies that have been presented... Writing...
3 Pages(750 words)Research Paper

SPSS EXERCISES

...SPSS Exercises December 18, SPSS Exercises Exercise 4 Pg. 328 Weight the data file by the number of cases Method of cooking potato chips Observed N Expected N Residual Fried in animal fat 7 16.0 -9.0 Fried in Canola oil 33 16.0 17.0 Baked 8 16.0 -8.0 Total 48 2. The output of the one-sample chi-square test to evaluate whether cooking method affects taste: Test Statistics Method of cooking potato chips Chi-Square 27.125a df 2 Asymp. Sig. .000 a. 0 cells (.0%) have expected frequencies less than 5. The minimum expected cell frequency is 16.0. a) Observed frequency for potato chips fried in Canola oil The frequency as evident from the SPSS output is 33 b) P value The P value is 0.000 c)...
3 Pages(750 words)Assignment

Phonetic exercises

...and meaning attached to them and so sounds give melody to language. The right intonation of sounds can convey a host of human feelings such as empathy, anger. Sounds can show confidence or certainty of our words. This course has helped me a appreciate the two fold meaning that sound can bring into one sentence through the use of word stress and sentence intonations to alter meaning. e. The importance of contrastive or comparative studies and the ability to construct exercises for learners of English as a second language. Constructing exercises for learners of English as a second language is now easier because of the emphasis I have learned that phonetics play on the meaning and the message sentences...
4 Pages(1000 words)Essay
sponsored ads
We use cookies to create the best experience for you. Keep on browsing if you are OK with that, or find out how to manage cookies.

Let us find you another Math Problem on topic Math Exercises for FREE!

Contact Us