Consider the project with the listed activities. Normal durations and costs, as well as crash durations and costs are listed for each activity. Precedence relationships are implicitly given by the activity names (e.g., activity (1,2) is represented as an arc from node 1 to node 2).
                                Crash     Crash                                     Normal                 Normal

Activity                 Time      Cost                                       Time                      Cost

(1, 2)                      5              $41,000                                 8                              $29,000

(1, 3)                      2              $18,000                                 3                              $10,000

(2, 4)                      10           $50,000                                 12                           $46,000

(2, 5)                      4              $26,000                                 6                              $20,000

(3, 5)                      9              $18,000                                 11                           $15,000

(4, 6)                      4              $22,000                                 5                              $20,000

(5, 6)                      4              $13,000                                 4                              $13,000

(5, 7)                      8              $30,000                                 10                           $25,000

(6, 8)                      3              $15,000                                 5                              $10,000

(7, 8)                      4              $10,000                                 5                              $7,000

*Times are in weeks

(a) Assuming that all activities are completed according to their normal durations, how long will it take to complete the project?

(b) Suppose that you wanted to shorten the duration of the project by 3 weeks. Which activities would you shorten, and by how much? What additional cost would you incur by doing this?

Task: Craps is a popular game played in casinos. Design a program using Raptor Flowcharts to play a variation of the game, as follows:

Roll two dice. Each dice has six faces representing values 1, 2, 3, 4, 5, and 6, respectively. Check the sum of the two dice. If the sum is 2, 3, or 12(called craps), you loose; if the sum is 7 or 11(called natural), you win; if the sum is another value(i.e., 4, 5, 6, 8, 9, or 10), a point is established. Continue roll the dice again, if the same point value is rolled, you win, otherwise, you loose. Please use Raptor Flowcharts to make the program

Your program should allow user play as many runs as wanted and display each run status and result. And display total number of runs user played and number of runs user won.

Here is a sample output:

Run 1:

You rolled 5 + 6 = 11

You Win!!!

Run 2:

You rolled 1 + 3 = 4

Point is 4, you have another try to win this run.

Rolled Again 2 + 4 = 6

You loose

Run 3:

You rolled 4 + 4 = 8

Point is 8, you have another try to win this run.

Rolled Again 2 + 6 = 8

You win!

Run 4:

You rolled 6 + 6 = 12

You loose

Total Runs: 4

User Won 2 of the 4 runs.

Tony wants to buy a new collar for each of his 4 dogs. The collars come in a choice of 5 different colors.

Step 1 of 2 :  

How many selections of collars for the 4 dogs are possible if repetitions of colors ARE ALLOWED?

Step 2 of 2:

How many selections of collars for the 4 dogs are possible if repetitions of colors ARE NOT ALLOWED?

Find the solution of the following problems. Before doing these problems, you might want to review Exercise 3** on page 63:

d.) xy" + y' = x, where y(1) = 1m and y'(1) = -1 (answer should be y(x) = 1/4 x² - 3/2 ln(x) + 3/4)

e.) (x-1)²y" + (x-1)y' - y = 0, where y(2) = 1, and y'(2) = 0 (answer should be: y(x) = 1/2 (x-1)^-1 + x/2 - 1/2)

**Exercise 3: The formula for a particular solution given in (3.42) applies to the more general problem of solving y" + p(t)y' + q(t)y = f(t). In this case, y₁ and y₂ are independent solutions of the associated homogeneous equation y" + p(t)y' + q(t)y = 0.

Please show work!

in java code

In the class Hw2, write a method removeDuplicates that given a sorted array, (1) removes the duplicates so that each distinct element appears exactly once in the sorted order at beginning of the original array, and (2) returns the number of distinct elements in the array. The following is the header of the method:

public static int removeDuplicates(int[ ] A)

For example, on input A=0, 0, 1, 1, 1, 2, 2, 3, 3, 4, your method should:

• Return 5 as the number of distinct elements.

• Have distinct elements 0, 1, 2, 3, 4 occupy the first 5 slots of the original array A. That is, after the method, the array A should look like A=0, 1, 2, 3, 4, *, *, *, *, *, where each * is a “don’t care”, that is, we don’t care what element occupies that slot.

Your method must have time complexity On and space complexity O1, where n is the length of the input array.

Hint: Use two pointers.

#1 Part 1: Find the payback in years (to the nearest hundredths place) for the following cash flow with a WACC of 4%:

Time Period                 Cash Flow                   Cumulative Out of Pocket

       0                                -100                                         -100

       1                                   40                                           -60

       2                                   50                                           -10

       3                                   20                                          +10

       4                                   70                                          +80

#1 Part 2: Find the discounted payback in years (to the nearest hundredths place) for the following cash flow with a WACC of 12%. Hint: interpolation must be used and I have started the table for you.

Time Period                 Cash Flow                   PV of Cash Flow        Cumulative

         0                              -100                              -100                           -100

         1                                  40                             35.71                        -64.29

         2                                  50                                    ?                                 ?

         3                                  20                                    ?                                 ?

         4                                  70                                    ?                                 ?                       

Reminder, your payback numbers are in units of years.

#2 Calculate the MIRR of the cash flows of the project below. Assume both the finance rate and the reinvestment rate are 5%

Time Period                 Cash Flow

         0                             -100

         1                                20

         2                                80

         3                                90

Paper trim problem: The Oblivion Paper Company produces rolls of paper for use in adding machines, desk calculators, and cash registers. The rolls, which are 200 feet long, are produced in widths of 1½, 2½, and 3½ inches. The production process provides 200-foot rolls in 10-inch widths only. The firm must therefore cut the rolls to the desired final product sizes. The five cutting alternatives and the amount of waste generated by each are as follows:

1 6 0 0 1

2 0 1 2 0.5

3 1 3 0 1

4 1 2 1 0

5 4 0 1 0.5

The minimum product requirements for the three products are as follows:

With the goal of minimizing the number of units of the 10-inch rolls will be processed on each cutting alternative, find each of the following:
Total Number of 10-inch Rolls Processed =

Note: Value is between 2485 and 2535

Number of 1½ inch rolls produced =

Number of 2½ inch rolls produced =

Number of 3½ inch rolls produced =

Number of Rolls Cut Using Alternative 1 =

Number of Rolls Cut Using Alternative 4 =

Number of Rolls Cut Using Alternative 5 =

*******Complete in Excel and show Formulas*******

Paper trim problem: The Oblivion Paper Company produces rolls of paper for use in adding machines, desk calculators, and cash registers. The rolls, which are 200 feet long, are produced in widths of 1½, 2½, and 3½ inches. The production process provides 200-foot rolls in 10-inch widths only. The firm must therefore cut the rolls to the desired final product sizes. The five cutting alternatives and the amount of waste generated by each are as follows:

The minimum product requirements for the three products are as follows:

With the goal of minimizing the number of units of the 10-inch rolls will be processed on each cutting alternative, find each of the following:
Total Number of 10-inch Rolls Processed =

Note: Value is between 1360 and 1390
Number of 1½ inch rolls produced =

Number of 2½ inch rolls produced =

Number of 3½ inch rolls produced =

Number of Rolls Cut Using Alternative 1 =

Number of Rolls Cut Using Alternative 4 =

Number of Rolls Cut Using Alternative 5 =