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Consider the linear optimization problem with inputs x, y and constraints
x + 2y ≤ 10
x + y ≤ 7
x ≤ 6
x ≥ -1
y ≥ 0
and a profit function
f(x, y) = 2x - 4y
(a) Draw the feasible region C for this optimization problem in the x, y-plane. (Hint: Allow space on the x-axis from -5 to 12 and on the y-axis from -3 to 8.)
(b) Find the vertices of C
(c) Find the maximum value and the minimum value of the profit function f(x, y) among all (x, y) ∈ C.
For the following algorithm find the number of times the assignment statement (:=) is executed during the running of the program. Answer the question by giving a formula in terms of n:
Ben has a cellphone plan that provides 200 free minutes each month for a flat rate of $39. For any minutes over 200 Ben is charged $0.35 per minute. Create a piecewise function that accurately represents Ben's charges based on his cellphone plan.
Use this result to prove that languages exist that are not recognizable by an oracle Turing machine with oracle for ATM.
Do we have obligations to future generations? Do our obligations extend beyond the living to future generations? If so, who speaks on behalf of future generations in business decision making?
Using the quadratic regression equation Predict the average county taxes for a house that is 20 years old.
find the equations of the bisectors of the angles between the lines 4x3y-120 and
A rock is thrown upward from the edge of a cliff. The rock follows the equation below. s = [b] x [d] + 64t - 16t2 What is the greatest height above the ground that this rock will go
Consider a sequence of Bernoulli trials X1, X2, X3,..., when Xn =1 or 0. Assume Pr{Xn=1 l X1, X2, ..., X(n-1)} >= alpha > 0, n=1,2,... Prove that : a) Pr{Xn =1 for some n} = 1 b) Pr{Xn =1 infinitely often} =1
Desribe the importance of quadratic equations to a basketball player, a diver, or even a sniper. Give an example of a real world situtation where you would apply quadratic equations.
The exterior angles of a triangle measure
1. What does Coca-Cola stand for? Is it the same for everyone? Explain. 2. Coca-Cola has successfully marketed to billions of people around the world. Why is it so successful? 3. Can Pepsi or any other company ever surpass Coca- Cola? Why or why not?..
Find the vertical velocity of the package for t = 8.0 min.
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