The objective function for a linear optimization problem is: Max ...

[Cooldude101]

The objective function for a linear optimization problem is: Max 3x + 2y, with one of the constraints being x and y both only take the values 0, 1 . Also x and y are the only decision variables. This is an example of a
 a. nonlinear program.
  b. mixed-integer linear program.
  c. LP relaxation of the integer linear program.
  d. binary integer linear program.

Question 2

A student wants to determine if pennies are really fair, meaning equally likely to land heads up or tails up. He flips a random sample of 50 pennies and finds that 28 of them land heads up. What are the appropriate null and alternative hypotheses?
 a. H0: p  0.5, Ha : p < 0.5
  b. H0: p  0.5, Ha : p  0.5
  c. H0: p = 0.5, Ha : p > 0.5
  d. H0: p  28, Ha : p < 28

[joewallace]

Answer to Question 1

d
RATIONALE: In some applications, the integer variables may take on only the values 0 or 1 . Then we have a binary integer linear program.

Answer to Question 2

c
RATIONALE: The appropriate null and alternative hypotheses are H0 : p = 0.5, Ha : p  0.5 . This is equivalent to saying pennies are fair vs pennies are not fair.