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1) Create a realistic business scenario. Give a brief description of the business and product sold and describe how many units were sold at 2 price points (say regular price or sale price, etc.)
2) Find demand equation based on 2 given price points and amounts sold.
Hint: you can form a linear equation based on 2 points of the form (x, p) or (p, x) where p - selling price of the product and x - number of items sold. Make sure to use appropriate notation (equation should either be in terms of p or x)
3) Find Revenue equation based on demand above.
4) Find either optimal price or number of items sold (based on your set-up) that gives maximum revenue using calculus (make sure to test critical value you find using 1st or 2nd derivative test). What is the maximum revenue?
5) What is the optimal price or number of items sold (find the other variable)? Is the result realistic? Why or why not?
Dividing a complex number with another number
1. Find the number of different ways to draw a 4-of-a-kind hand from a standard 52 card deck, i.e. X X X X Y where the X's are four cards of the same rank (A to 2) and Y differs from X in rank. (Note: there are 4 suits per rank.) Let's think this ..
Use chain rule to verify that every function of the form. Then use this fact to find the solution which also satisfies the initial conditions:
A nuclear tower is a hyperboloid that is a hyperbola rotated around its conjugate axis. The equation of hyperbola is X^2/100^2 - y^2/150^2 = 1. The tower is 500 feet tall, the top is 150 feet above the center of the hyperbola and the base is 350 f..
The perimeter of a regulation singles tennis court is 210 feet and the length is 3 feet less than three times the width. What are the dimensions of the court?
using trigonometry to solve a right triangle.the angle of depression to one side of a lake measured from the passenger
Estimate the model where house prices are affected by rail distance only. What is the sign and magnitude of the coefficient on rail distance, and what is the fit of the regression
Use geometric techniques to estimate the percentage full. Find an upper and lower bound to the percentage full.
Estimate the approximate population of Appleville in 1988 by finding an equation and then substituting.
Describe the object, include details on how you went about performing the calculation, and determine the slope. Be sure to include the unit of measurement (inches, feet, yards, etc.).
Determine the asymptotic stability of the system x' = Ax where. More specifically, what stability conclusion(s) can be drawn?
Find location of the point P that allows bird to complete its journey in the minimum time (solve for x). Minimizing Travel Time A woman is on a lake in a rowboat located 1 mi from the closest point P of a straight shoreline.
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