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 +...

...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....

...*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."
Opportunity...

...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...

...particular function, dy/dx = 4x - 3. If it is known that when x = 1, y = 5, find y in 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?...

...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
...

...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...

...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...