What is the relationship between decision variables and the objective function?
What is the difference between an objective function and a constraint?
Does the linear programming approach apply the same way in different applications? Explain why or why not using examples.

1. Determine whether each of the following is a function or not.
(a) f(x) = 1 if x>1
= 0 otherwise
(b) f(x) = 2 if x>0
= -2 if x<0
= 2 or -2 if x = 0
= 0 otherwise
(c) f(x) = 5/x
2. Suppose you have a lemonade stand, and when you charge $1 per cup of lemonade you se

1. Suppose I had a lemonade stand. When I charge $1, I sold 50 cups, when I raised the price to $2, I only sold 25 cups. Write an equation for the number of cups I sold as a function of the price i charged. Denote C for number of cups and P for price. Assume the function is linear.
2. Write an equation for f(x) based on x -2,

3.88
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Use your answer from 3.87 to showthat E(Y) = aE(X) +b
3.87: [ If X is a random variable with moment-generating function M(t), and Y is a function of X given by Y=aX+b,
showthat the moment-generating functionfor Y is e^(tb) * M(at) ]
My answer for exercise 3.87 is attached.

#4. The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by
f (x) = 10/x2 x > 10
f (x) = 0 x ≤ 10
(a) Find P{X > 20}.
(b) What is cumulative distribution function of X?
.. (see attachment)

3)
x -2 -1 0 1 2
y .25 .5 1 2 4
Given the table above, graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, and give the domain and range as shown in the graph, and also the domain and range of the entirefunction.
Graph
Graph Type
Explanation
D

One of the advantages of rational functions is that even rational functions with low-order polynomials can provide an excellent fit forcomplex experimental data. Linear-to-linear rational functions have been used to describe earthquake plates.
As another example, a linear-quadratic fit has been used to describe lung functio

Evaluate the functions for the value of x given as 1,2,4,8,and 16. Describe the difference in the rate at which each function changes with increasing value of x; rank the function from fastest-growing to slowest-growing?
1) f(x)=3x+2
2) f(x)=x^2+5x+6
3) f(x)=x^3+3x^2+2x+1
4) f(x)=e^x
5) f(x)=log x