Investigation Draft IIAsif Sarker
12/25/12
Asif’s Backscratchers Inc.

Problem: Asif runs a big modern day company that is like any other. The company sells quantities of products that are plastic backscratchers. The company right now is failing severely because there are much more products being made then being sold and we need a way to find out how to find the number of production level that will maximize a company’s profit.

We are given that the Total money the company spends is 840 + 10.26x - 0.0541x2 + 0.0007x3 And the Profit we are making from this amount of quantities are 30.5 – 0.001x + 10.004x2

So what do we know so far? What kind of math can be used? The answer is derivatives. Usually you learn about derivatives in pre calc when you first learn about finding slopes of tangent lines right? Your teacher goes to tell you that derivatives are the regularly seen as a method finding the slope of a point for a function. But more importantly Derivatives runs our society. If you are thinking “oh the big companies and the rich white people run our society”, then you are right. These people know their calculus and use it to become rich. Derivatives are pretty simple for polynomials. To find the derivative of a polynomial you use the power rule. There are many other rules that can be used for other types of functions.

The proof for the power rules:
Historically the power rule was derived from Cavalieri’s quadrature formula which is when the area under Xn for any integer n≥ 0. But nowadays the power rule is derived first and integration considered as its inverse. For[pic], the derivative of [pic] is [pic]

That is [pic]
To prove the power rule for differentiation, we use the definition of the derivative as a limit. [pic]

Now you know what derivatives are; one important application of derivatives is on marketing, mostly on marginal revenue and marginal cost. Marginal revenue and Marginal costs are derivatives. The marginal...

...Economics 5315 Fall 1999
Managerial Economics Professor Henderson
Final Exam
1. The Zinger Company manufactures and sells a line of sewing machines. Monthly demand for one its most popular models is given by the following relationship:
Q = 400 – 0.5P
where P is price and Q is quantity demanded. Total costs of production (including a “normal” return on owners’ investment) per month are:
C = 20,000 + 50Q + 3Q2
a. Express total profits (() in terms of Q.
b. At what level of output are total profits maximized? What price will be charged? What are total profits at this output level?
c. What market structure did you assume? Why?
d. Would your answers in b change if the market for sewing machines were competitive? How? (Specify price, quantity, and profit levels.)
2. Zar Island Gas Company is the sole producer of natural gas in the remote island country of Zar. The State Energy Commission regulates the company’s operations. The demand function for gas in Zar has been estimated as:
P = 1,000 – 0.2Q
where Q is output (measured in gas units) and P is price (measured in dollars per gas unit). Zar Island’s cost function is:
C = 300,000 + 10Q
This cost function does not include a “normal” return on the firm’s invested capital of $4 million.
a. In...

...the average variable cost is
a. at the same level of output as the minimum average total cost
b. at a smaller level of output than the minimum average total cost
c. at a larger level of output than the minimum average total cost
d. at the same level of output as the average fixed costs
e. same as minimum marginalcost
2. The multiplant monopolist maximises profits when
a. Marginalcost equals marginal revenue
b. When marginalcost in each plant are equal
c. When average cost in each plant is equal
d. When marginal revenue in each plant is zero
e. When he produces only in the low cost plant
3. If the market price is exactly equal to average cost,
a. the firm shuts down as there is no profit
b. the firm shuts down as the variable costs cannot be covered
c. Continues to operate in the short run
d. The firm shuts down as it cannot cover its fixed
e. The firm shuts down if the price is lower than average variable cost
4. Which of the following would shift a firms short run average cost upward
a. An advance in technology
b. An increase in wages
c. An increase in demand for the product
d. Reduction in excise taxes
e. Reduction in interest costs...

...1. *Define scarcity and opportunity cost. What role these two concepts play in the making of business decisions?
Scarcity is a Ever-present situation in all markets whereby either less goods are available than the demand for them, or only too little money is available to their potential buyers for making the purchase. This universal phenomenon leads to the definition of economics as the "science of allocation of scarce resources."
Opportunitycost is the cost of an alternative that must be forgone in order to pursue a certain action. Put another way, the benefits you could have received by taking an alternative action.
Opportunity cost can be defined as the value of the next best alternative forgone. It can be defined as the revenue or the profit that a person/organization would have been able to earn if it had exercised the alternative decision instead of the decision that has been made.
Opportunity-cost has many practical business applications, because opportunity costs will exist as long as resource scarcity exists. The value of the next-best alternative should be considered when choosing among production possibilities, calculating the cost of capital, analyzing comparative advantages, and even choosing which product to buy or how to spend time.
2. *(a) what is Marginal Analysis? (b) Why Is...

...Hi Jacqueline, Professor and class
You were able to deliver a great post easy to comprehend. Regarding the topic this week, you’ve mentioned the fact that the number of goods that a firm is manufacturing is in direct connection with the marginal product. Sometimes, less is more and less employees using the right equipment and technologies are able to perform much efficient that a greater number of employees that are using old tools in their activity. .
As you well said,marginalcost and marginal product are strongly connected. When the value of the marginalcost is dropping, the value of the marginal product is raising and vice-versa. The quantity of the inputs can’t be changed at one time so managers tend to keep some of the inputs at a constant level. As every manager is looking to earn and increase profit, it is very important to calculate and determine the level at which the rate of profit is going to reach a maximum value. (www.ag.ndsu.edu).
Considering that you’re working as a manager and get across a negative value for the marginal product of labor, what would you consider the cause might be?
References
Diminishing Marginal Productivity — NDSU. (n.d). NDSU Agriculture — NDSU. Retrieved September 22, 2013, from http://www.ag.ndsu.edu/aglawandmanage
Hi Lisset, Professor and class
Thanks a lot...

...terms of x.
6. A manufacturing process costs RM 6500 to set up for one year’s use. If items cost RM 85 each to produce and other costs amount to 3.5 x2, where x is the production in hundreds, find the level of production that will minimise the cost per item over the year. What will the total cost amount to at this level of production?
7. The marketing department of Spager Ltd estimated that if the selling price of product is set at $15 per unit then the sales will be 50 units per week, while, if the selling price is set at $20 per unit, the sales will be 30 units per week. Assume that the graph of this function is linear. The production department estimates that the variable cost will be $5 per unit and that the fixed cost will be $50 per week, and special cost are estimated as $0.125x2, where x is the quantity of output. All production is sold.
(a) Show that the relationship between price (Pr) and quantity sold (x) , are given by the equation Pr = 27.5 - 0.25x.
(b) Find the revenue function, R.
(c) Find the total cost function (C).
(d) Advise the company on production and pricing policy if it wishes to maximize profits, and find the maximum profit.
8. A firm receives £135 for each unit sold. The costs consist of a fixed cost per month of £2500...

...3.05 MarginalCost Analysis
Name:______________________________________________
Step One: Launch the data generator to get started (located in the last page of the lesson, or use the numbers given below:
Quantity
Price (in whole dollars)
Total Revenue
Marginal Revenue
Total CostMarginalCostProfit (or loss)
0
42
0
35
1
41
41
68
2
40
80
94
3
39
117
107
4
38
152
114
5
37
185
129
6
36
216
180
7
35
245
235
8
34
272
296
Step Two: Determine a product market (a specific good or service) appropriate to the prices listed. This will be the title of your graph and data table. You will be creating a graph on Step Four.
Step Three: Calculate the marginal revenue, marginalcost, and profit for each quantity level. Fill in the data table. Use the Case Study presentation at the bottom of the lesson page in 3.05 for step by step instructions on how to calculate your figures. This case will also help you construct your Step Four.
o Total Revenue = Quantity x Price
o Total Cost = Fixed Cost + Variable Cost
o Profit or Loss = Total Revenue – Total Cost
o ―Marginal means additional
o Marginal Revenue is computed by finding the difference of the previous two quantities (total revenue of...

...SD – MBA 2
Personal Report
Name: Thuy Anh Nguyen
November 6,2012
1. Conditions for profit maximization are:
a) Difference between total revenue (TR) and total cost (TC) is maximized;
b) Marginal revenue (MR) should be equal to marginalcost (MC)
Explanations: If we assume that the company is facing a downward – sloping curve and it produces just one single product
a) Profit = TR – TC.Profit will increase if TR increases and TC decreases. If company wants profit maximization, it should be TR maximization and TC minimization. The maximized difference between TR maximization and TC minimization is profit maximization.
b) MR = MC
- This comes from the function: Marginalprofit = marginal revenue (MR) - marginalcost (MC). When MR is more than MC, marginalprofit is positive, when MR is down to the extent that it is smaller than MC, marginalprofit is negative. When marginalprofit is too positive (that’s meant the price is too high, or too negative (that’s meant the price is very low, thus the quality is thought to be bad), it gets a maximum where MR = 0.
- If we illustrate in a figure , this only happens at the point where MR cuts MC. The total profit area is...

...Marginal Revenue and MarginalCost
An understanding of marginal revenue and marginalcost is economically crucial to owning and operating a successful business. Marginal revenue is the amount of change in total revenue by selling one additional product. So if a company sells four extra unit of product and brings extra total revenue of 500 dollars than the marginal revenue for this month would be 125 dollars. This is found by taking the change in total revenue, 500 dollars, and dividing it by the change in quantity, 4 units of product. This gives you the marginal revenue which can help a company understand what each unit is worth and how much they will be making for each extra unit.
Marginalcost is how much it cost the company to produce one more product. A company calculates the marginalcost by taking the change in total cost and dividing it by the change in quantity. If it cost a company 400 dollars to produce eight units and it cost a company 425 dollars to produce nine units than the marginalcost for making product nine is 25 dollars.
Finding a profit and understanding when you are earning a profit is crucial because this defines how much your company with gross every...