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(i) Given a demand function D=150-2x and a supply function S=8x where x is price, find the (x, y) coordinates of the equilibrium point. Also, graph the demand and supply function on a single graph and label the equilibrium point on your graph.
(ii) Items cost $4 each to produce and sell for $20 each. The overhead is $1200. a) Find the cost, revenue and profit functions. b) Find the (x, y) coordinates of the breakeven point. Also graph the cost and revenue functions on the same graph and indicate the breakeven point.
Jack and Jill decide to have a four-lap race (i.e. 4 m meters) with each runner agreeing to run only in his/her lane. If Jack runs in lane two, how far ahead of jill should be begin if the finish line is jill's starting point?
If the locker is closed, he or she opens it. If it is opened, he or she closes it. This process continues with the fourth student, fifth student, and so on. How many lockers are opened after 5000 students?
alan is building a garden shaped like a rectangle with a semicircle attached to one short side. if he has 60 feet of fencing to go around it, what dimensions will give him the maximum area in the garden?
A student received the following grades: An A in Statistics (4 credits), a F in Physics II (5 credits), a B in Sociology (3 credits), a B in a Literature seminar (2 credits), and a D in Tennis (1 credit). Assuming A = 4 grade points, B = 3 grade poi..
Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the region the integral represents
Lisa has a basketball court that is 30 feet long and has a perimeter of 106 feet. How wide is the court?
A small business buys a computer for $3700. After 4 years the value of the computer is expected to be $200. For accounting purposes the business uses linear depreciation to assess the value of the computer at a given time.
dimensions of a rectangle where its length is 11 more than its width. If the lenght was doubled and width decreased by 5 the area would be increased by 72 in squared what are the length and side eimdension.
Suppose that X and Y are two mathematical objects of the same sort (two sets, two rings, etc.), and we consider the family of all homomorphisms among them. What structure does this system have?
Write the statement about an improper integral that, you have derived in part (a), [what the improper integral it. is; convergent or divergent; what its value is if convergent.]
The volume of a cylinder(think about the volume of a can)is given by v=pir^2h where r is the radius of the cylinder and h is the height of the cylinder.
Formulate a mathematical program that can be used to determine where the "hub" should be located in the plane. Clearly define your decision variables, objective and constraints
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