1.Differentiate the following:
(a)y = 10 x3 - 10 x2 + 4x + 2(e)y = [pic]
(b)y = [pic](f)y = ( 4 + x ) ( x - 1 )
(c)y = [pic](g)2y = 3 x2 + 10
(d)y =[pic](h)x y = 2 x2 - 5 x + 4

2.Find the integral of the following:
(a) [pic](e)[pic]
(b) [pic](f) [pic]
(c) [pic](g) [pic]
(d) [pic]

3.Find the x value of the turning points on the graph of y = [pic] and determine whether it is a maximum or a minimun point.

4.Find the coordinates of the two turning points of the function y = x3 - 8 x2 + 5 x + 3

5.For a 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?

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 and...

...market power. Apply the quantity and price affects on revenue of any movement along a demand curve. Find the profit maximizing quantity and price of a single-price monopolist. Compute deadweight loss from a single-price monopolist. Compute marginal revenue. Define the efficiency of P = MC. Find the profit-maximizing quantity and price of a perfect-price-discriminating monopolist. Find the profit-maximizing quantity and price of an imperfect-price-discriminating...

...You have determined that the service (Z) provided by BF is a function of its medical staff input (M) and sound service input (S) which is given by:
Z = M + .5S + .5 MS - S2
BF’s staff budget for the coming year is $1,200,000. Annual employment costs are $30,000 for each social service staff member (S) and $60,000 for each medical staff member (M).
(1iiia) Using the Lagrangean multiplier approach calculate the optimal (i.e., service maximizing) combination of medical and...

...the following would tend to make demand INELASTIC?
Selected Answer: Correct Answer:
5 out of 5 points
the proportion of the budget spent on the item is very small the proportion of the budget spent on the item is very small
Question 10
Marginal revenue (MR) is ____ when total revenue is maximized.
Selected Answer: Correct Answer:
5 out of 5 points
equal to zero equal to zero
Question 11
5 out of 5 points
Empirical estimates of the price elasticity of...

...MARGINAL PRODUCTIVITY THEORY:
A theory used to analyze the profit-maximizing quantity of inputs (that is, the services of factor of productions) purchased by a firm in the production of output. Marginal-productivity theory indicates that the demand for a factor of production is based on the marginal product of the factor. In particular, a firm is generally willing to pay a higher price for an input that is more productive and contributes more to...

...“Apply the concepts of marginal utility theory, product differentiation, and revenue/profit maximization to some event in your personal, daily lives.” [1]
Marginal Utility Concept Application
From the three concepts at hand this is by far the easiest to exemplify. According to Sloman and Sutcliffe the concept of utility is directly related to that of satisfaction [2]. The satisfaction that one individual takes from consuming something is called utility....

...Wikipedia, the free encyclopedia
An oligopoly is a market form in which a market or industry is dominated by a small number of sellers (oligopolists). Oligopolies can result from various forms of collusion which reduce competition and lead to higher costs for consumers. [1]
With few sellers, each oligopolist is likely to be aware of the actions of the others. The decisions of one firm therefore influence and are influenced by the decisions of other firms. Strategic planning by...

...*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 cost is...

...power in the provision of this good. What is true of the relationship between the price of this resource and the marginal revenue the firm receives?
25-1 (a)
The demand curve faced by the firm is the downward-sloping market demand curve, so price exceeds marginal revenue at all quantities beyond the first unit produced.
25-3
The following table depicts the daily output, price, and costs of a monopoly dry cleaner located near the campus of a...