One common system for computing a grade point average​ (GPA) assigns 4 points to an​ A, 3 points to a​ B, 2 points to a​ C, 1 point to a​ D, and 0 points to an F. What is the GPA of a student who gets an A in a 3​-credit ​course, a B in each of two 2​-credit ​courses, a C in a 3​-credit ​course, and a D in a 4​-credit ​course? The mean grade point score is

Maximize Z= 3 X1+4 X2+2.5X3

Subject to

3X1+4X2+2X3≤500

2X1+1X2+2X3≤400

1X1+3X2+3X3≤300

X1,X2,X3≥0

Change objective function coeffiecient x3 to 6 and change coefficient of x3 to 5in constraint 1 ,to 2 in constraint 2 ,to 4 in constraint3. calculate new optimal solution using sensitivity analysis

Use pigeonhole principle to prove the following (need to identify pigeons/objects and pigeonholes/boxes):

a. How many cards must be drawn from a standard 52-card deck to guarantee 2 cards of the same suit? (Note that there are 4 suits.)

b. Prove that if four numbers are chosen from the set {1, 2, 3, 4, 5, 6}, at least one pair must add up to 7.

An inflation-indexed 3-year, annual 4% coupon bond issued by Thailand at par (Present Value =Par Value = 100 Thai Bhat initially). Inflation in Thailand increases by 5 % in year 1, by 4 % in year 2, and zero % in year 3. What is the coupon amount in Thai Bhat in year 2?

a. Bhat 4.20

b. Bhat 4.00

c. Bhat 5.00

d. Bhat 4.37

Falwell Company, as lessee, enters into a lease agreement on January 1, 2018, for equipment. The following data are relevant to the lease agreement:

1.         The term of the noncancelable lease is 4 years. Payments of $4,892 are due on January 1 of each year.

2.         The fair value of the equipment on January 1, 2018 is $25,000 and the book value is 20,000. The equipment has an economic life of 6 years. Both parties expect the equipment to have an unguaranteed residual value of $8,250 at the end of the lease term. The equipment reverts to the lessor at the end of the lease term. The equipment is not of a specialized nature and there is no purchase option.

3.         The lessee pays all executory costs.

4.         The interest rate implicit in the lease is 5% and known to Falwell.

1. Indicate the type of lease FalwellCompany has entered into and what accounting treatment is applicable.

(b)    Prepare lease amortization schedule (s) for Falwell Company for the first three years.

(c)    Prepare the journal entries on Falwell’s books that relate to the lease agreement for the following dates:

        1.    January 1, 2018.

        2.    December 31, 2018.

        3.    January 1, 2019.

        4.    December 31, 2019.

1. Cash Payback Period, A method of analysis of proposed capital investments that focuses on the present value of the cash flows expected from the investments.Net Present Value Method, and Analysis

   Elite Apparel Inc. is considering two investment projects. The estimated net cash flows from each project are as follows:

   Year	Plant Expansion		Retail Store Expansion
   1	$150,000		$125,000
   2	122,000		147,000
   3	106,000		101,000
   4	96,000		70,000
   5	29,000		60,000
   Total	$503,000		$503,000

   Each project requires an investment of $272,000. A rate of 15% has been selected for the net present value analysis.

   Present Value of $1 at Compound Interest
   Year	6%	10%	12%	15%	20%
   1	0.943	0.909	0.893	0.870	0.833
   2	0.890	0.826	0.797	0.756	0.694
   3	0.840	0.751	0.712	0.658	0.579
   4	0.792	0.683	0.636	0.572	0.482
   5	0.747	0.621	0.567	0.497	0.402
   6	0.705	0.564	0.507	0.432	0.335
   7	0.665	0.513	0.452	0.376	0.279
   8	0.627	0.467	0.404	0.327	0.233
   9	0.592	0.424	0.361	0.284	0.194
   10	0.558	0.386	0.322	0.247	0.162

   Required:

   1a. Compute the cash payback period for each project.

   	Cash Payback Period
   Plant Expansion	2 years 1 year 2 years 3 years 4 years 5 years
   Retail Store Expansion	2 years 1 year 2 years 3 years 4 years 5 years

   1b. Compute the net present value. Use the present value of $1 table above. If required, round to the nearest dollar.

   	Plant Expansion	Retail Store Expansion
   Total present value of net cash flow	$	$
   Less amount to be invested
   Net present value	$	$

Use the following information for questions 1-5.

Do larger families spend more per week on food? A sample of 10 families in Chicago revealed the following data for family size and the weekly grocery bill. (Part of the calculations are done for you.)

           Family size     $Groceries     (X-Xbar)        (Y-Ybar)       (X-Xbar) x (Y-Ybar)

•          3                 99                -1                 -11                        11
•          6                114                2                    4                          8
•          5                131                1                   21                       21
•          6                129                2                   19                       38
•          6                142                2                   32                       64
•          3                111               -1                    1                       
•          4                104                0
•          2                  81
•          2                  98
•          3                  91
•         40             1100

Sx = 1.63     Sy = 19.28     X-bar = 40/10 = 4    Y-bar = 1100/10 = 110

Grocery Question #1: Calculate ∑ (X - Xbar) x (Y - Ybar)

Grocery Question #2: Assuming that ∑ (X - Xbar) x (Y - Ybar) is equal to 242, calculate r.

Grocery Question #3: Assuming that r = +0.856, determine the regression equation,

Grocery Question #4: Assuming that the Regression equation is Y = 70 + .858X, how much would you expect a family of five to spend on groceries over a week's time?

Grocery Question #5: Assuming that the coefficient of determination is 0.732, what conclusion can you reach?

1. If the economy is initially at a long run equilibrium, take each situation given below one by one and answer all four following questions for each of them by filling the blanks in the table below. (Hint: Always compare the change in the variable from initial position. Drawing the graphs for each situation should help to understand the change in variables.)

1. Which curve is going to shift in which direction? (2×4)
2. Explain how each of these will affect the economy in the short run and the long run (in terms of output, unemployment and inflation) (6×4)
3. For each of the following what kind of monetary policy do you suggest? (1 ×4)
4. How does the policy affect the economy in terms of output, inflation and employment? (6×4)

• Situation 1: Government decides to take policy to reduce budget deficit. (budget deficit= Taxes – government expenditure)
• Situation 2: Construction workers goes on a strike for 2 months.
• Situation 3: US dollar depreciates with respect to euro. That makes the import more expensive and export cheaper.
• Situation 4: Productivity of U. S workers increase due to technological advancement.

Q1 Write a python regular expression to match a certain pattern of phone number.

            ### Suppose we want to recognize phone numbers with or without hyphens. The

### regular expression you give should work for any number of groups of any (non-

### empty) size, separated by 1 hyphen. Each group is [0-9]+.

### Hint: Accept "5" but not "-6"

### FSM for TELEPHONE NUMBER IS:

# state:1 --[0-9]--> state:2

# state:2 --[0-9]--> state:4

# state:2 --[\-]---> state:3

# state:3 --[0-9]--> state:4

# state:4 --[\-]---> state:3

# state:4 --[0-9]--> state:4

import re

regexp = ###Your Regular Expression Here.

### regexp matches:

print(re.findall(regexp,"123-4567") == ["123-4567"])

#>>> True

print(re.findall(regexp,"1234567") == ["1234567"])

#>>> True

print(re.findall(regexp,"08-78-88-88-88") == ["08-78-88-88-88"])

#>>> True

print(re.findall(regexp,"0878888888") == ["0878888888"])

#>>> True

### regexp does not match:

print(re.findall(regexp,"-6") != ["-6"])

#>>> True