A farmer has a 40-acre farm in Georgia. The farmer is trying to determine how many acres of corn, peanuts, and cotton to plant. Each crop requires labor, fertilizer, and insecticide. The farmer has developed the following linear programming model to determine the number of acres of corn (X1), peanuts (X2), and cotton (X3) to plant in order to maximize profit. Max 550 X1 350 X2 450 X3 s. t. Constraint 1: 2 X1 3 X2 2 X3

z (max) =  17461.54  $

x₁   =  29.23 acres

x₂  =  0

x₃  =  3.07

Step-by-step explanation: INCOMPLETE QUESTION.

As the problem statement establishes:  "Each crop requires labor, fertilizer, and insecticide"  and information about quantities and availability does not exist. To build a model and that such model would be feasible I copy from the internet the following data. We assume the problem is to maximize the number of acres to plant with a maximum of profit ( we will use as profit the numbers 550  ;  350 ; 450 for  acres of corn, peanuts, and cotton)

Then z =  550*x₁  +  350*x₂  +  450*x₃    to maximize

                                            labor (h)      fertilizer ( tn)    Insecticide (Tn)

acres of corn         (x₁)               2                     4                        3

acres of peanut     (x₂)              3                     3                        2

acres of cotton      (x₃)              2                     1                         4

Availability         acres 40       120                120                      100

Constraints:

1) Size of the farm 120 acres

x₁  +  x₂   +   x₃   ≤   40

2) labor   120 h

2*x₁  +  3*x₂  +  2*x₃    ≤   120

3) Fertilizer  120 Tn

4*x₁  +  3*x₂  +  1*x₃      ≤   120

4) Insecticide 100 Tn

3*x₁   +  2*x₂  +  4*x₃     ≤  100

The Model is:

z =  550*x₁  +  350*x₂  +  450*x₃    to maximize

Subject to:

x₁  +  x₂   +   x₃   ≤   40

2*x₁  +  3*x₂  +  2*x₃    ≤   120

4*x₁  +  3*x₂  +  1*x₃      ≤   120

3*x₁   +  2*x₂  +  4*x₃     ≤  100

x₁    ≥   0  ;   x₂   ≥   0  ;   x₃   ≥   0

After 3 iterations using an on-line solver optimal solution is:

z (max) =  17461.54  $

x₁   =  29.23 acres

x₂  =  0

x₃  =  3.07

x -

median = 1.25

range = 12-14.5

interquartile = q12-q14.5

y -

median = 1

range = 15-17

interquartile = q15-q17

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.