Financial Math Answers

Given below is a table obtained after a few iterations, using the simplex method to solve a linear programming problem to maximise the total contribution from product A and product B.
cj's : 8.5 10.5 0 0 0
Basic variables : X1 X2 S1 S2 S3
Quantity
X2 : 0 1 3/5 -2/5 0 300
X1 : 1 0 -2/5 3/5 0 300
S3 : 0 0 -1/5 -1/5 1 400
i) Is the solution above optimal? ii) Does the problem have an alternative solution? If so, find the other solution.

A bakery keeps a stock of a popular brand of bread. Previous experience indicates the daily demand as given below:
Daily demand Probability
0 0.01
10 0.20
20 0.15
30 0.50
40 0.12
50 0.02 Consider the following sequence of random numbes: 48, 78, 19, 51, 56, 77, 15, 14, 68, 09 Using this sequence, simulate the demand for the next 10 days.

Consider a 4/2/F/Fmax problem with the job processing time as given below:
Job Processing time on
Machine1 Machine2
A 6 10
B 8 5
C 14 8
D 7 2
i) Find the optimal sequence of jobs. ii) Find the total elapsed time.

A company produces three products, P1, P2, P3 from three raw materials A, B and C. One unit of product P1 requires one unit of A, 3 units of B and 2 units of C. A unit of product P2 requires two units each of A and B and 3 units of C, while one unit of P3 needs 2 units of A, 6 units of B and 4 units of C. The company has a daily availability of 8 units of A, 12 units of B and 12 units of C. It is further known that the profit per unit is Rs.3, Rs.2 and Rs.5 for P1, P2 and P3, respectively. How many units of product P1, product P2 and product P3 should the company manufacture to maximize the profit? Formulate this problem as a Linear programming problem.

Write down the dual of the LPP given by: Maximize 20x1 + 30x2 subject to:
x1 + 2x2 ≤ 20
x1 + x2 ≤ 12
5x1 + x2 ≤ 40
x1, x2 ≥ 0
Solve the primal LPP graphically. Use the optimal solution to primal LPP and complementary slackness condition to identify the dual variable that will have zero value in the optimal solution to the dual.

If a property value is increasing by 10% a year. How long will it take for the property value to double.

Find the principal invested if the simple interest earned in 5 years by an investment at 5% per annum is $100

Danny just answered a help-wanted ad. The ad states that the job pays $27 K annually. What would Danny’s monthly salary be if he gets the job?

Joy is considering taking AP classes or dual credit at the community college where she would receive an Associate’s Degree. Her parents pay no taxes and she is concerned with the expense of college. The classes she would take at the Community College would qualify her as a full-time student and would cost $106. If she took the AP class, she would qualify for free classes, but she needs to pay $92 for the national AP exam. Which education program should she use to reduce the cost of her education? Why? How much would she save?

Anna’s bank gives her a loan with a stated interest rate of 10.22%. How much greater will Anna’s effective interest rate be if the interest is compounded daily, rather than compounded monthly?