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Find the number of units x that produce a maximum revinue R.
R=800x-0.2x^2
R=48x^2-0.2x^3
Find the number of unites x that produce the minimum average cost per unit C.
C=1.25x^2+25x+8000
C=0.001x^3+5x+250
find the amounts of advertising that maximizes the profit P. (s and p are measeured in thousands of dollars.) Find the point of diminishing returns.
P= -2s^3+35s^2-100s+200
P=-0.1s^3+6s^2+400
Suppose that a license plate must contain a sequence of two-letters followed by four-digits, or three-letters followed by three-digits.
Graph the functions y=x and y= square root of x on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs.
A landscaper blends his own fertilizer which consists of four compounds at the listed price per lb: Formulate an LP problem to determine what blend of these compounds will minimize the cost of a 50lb bag of fertilizer given the following:
Let V be the volume of a sphere of radius r that is changing w/ respect to time. If dr/dt is constant, is dV/dt constant, explain. All edges of a cube are expanding at a rate of 3 centimeters per second. How fast is the volume changing when each ..
Let A be a symmetric and positive definite (SPD) matrix. Is A^-1 ( inverse of matrix A) a SPD matrix? If so, prove it. If not, explain and give an example.
What then is the chance that there will be a need for exactly 2 ambulances during that time slot on any given Wednesday morning?
Assume that a watermelon dropped from a tall building falls y=16t^2 in t sec. Find the watermelon's average speed during the first 3 sec of fall and the speed at the instant t=3sec.
Find the slope and the y-intercept of the line represented by the equation: 2x + y = 14. Write the equation of a line in slope-intercept form with the slope of -4/5 and y-intercept (0, -3)
You are told that a line is tangent to the circle centred at (3,2) with radius 2. If the tangent line and circle intersect at the point (4, 2+ sqrt(3)) find the equation of the tangent.
Find the p-value for each of the following hypothesis testing situations.
Compute the mean and variance for binomial distribution. Calculate the mean and standard deviation (by hand) for the binomial distribution with the probability of a success being 1/4, 1/2, 3/4.
Calculate distance from line through the outer summary points to the middle point. Equation of the median-median line of best fit for data. What is the slope?
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