Assignment #1: JET Copies Case Problem MAT 540 Quantitative Methods Professor Abdul Khan January 26, 2014 1. In Excel, use a suitable method for generating the number of days needed to repair the copier, when it is out of service, according to the discrete distribution shown. As for the first segment of the case, I needed to figure out the number of days needed in order to repair the copier. Initially, I assumed that the amount of days required to repair a copier is random. So with that, I could generate a random number using the Excel RAND function that I designated r2 between 0 and 1.
Each unit of part # 2206 is sold for $15. The unit production cost of part # 2206 is $3. The fixed monthly cost of operating the production facility is $3000. How many units of part # 2206 have to be sold in a month to break-even? Answer Selected Answer: 250 Correct Answer: 250 Question 9 0 out of 2 points A university is planning a seminar.
Read the "JET Copies" Case Problem on pages 678-679 of the text. Using simulation estimate the loss of revenue due to copier breakdown for one year, as follows: In Excel, use a suitable method for generating the number of days needed to repair the copier, when it is out of service, according to the discrete distribution shown. Repair Time P(Y) Cumulative RN Range 1 0.20 0.20 01-20 2 0.45 0.65 21-65 3 0.25 0.90 66-90 4 0.10 1.00 91-99,000 In Excel, use a suitable method for simulating the interval between successive breakdowns, according to the continuous distribution shown. In Excel, use a suitable method for simulating the lost revenue for each day the copier is out of service. Put all of this together to simulate the lost revenue due to copier breakdowns over 1 year to answer the question asked in the case study.
Read each question carefully The Final is 2 and 1/2 hours long or 150 minutes Homework and Quizzes: 150 pts Midterms: 550 pts Final Exam : 300 pts Final Grade over 1000 Letter Grade Note that you need at least 600/1000 to make a grade of C − . 1 Exercise 1. (30 points) If u = i − j + k and v = i + j + k • Find the cosine of the angle between the vectors u and v • For what values of the constant b are the vectors v orthogonal? and w = i + b j • Find the area of the parallelepiped spanned by the vectors u and v 2 Exercise 2. (30 points) • Find the vector equation of the line through P (2, 1, 3) perpendicular to the plane 3x − 4y + z − 5 = 0 • Two particles P1 and P2 have position vector r1 (t) =< 1, t + 3, −t > and r2 (t) =< 2t − 1, 1 + 3t2 , t3 − 2 > respectively at time t. Do the particles collide?
Located on page 304, problem #90 states, “P dollars is invested at annual interest rate r for 1 year. If the interest is compounded the polynomial P(1+r/2)2 represents the value of the investment after 1 year.” (Dugopolski, 2012, p.304) For the first part rewrite the expression without parenthesis. This would require the use of FOIL, which means multiply First, Outer, Inner, Last. Do this to the binomial (1+r/2)2 and then multiply all of the terms by P. The following is an example: P(1+r/2)2 This is the original expression with the exponent ONLY with the binomial. P(1+r/2)(1+r/2) Next step is to multiply the squared quantity.
Quarter 2 Project: Matrices: 3 10 1 8 row1column1= 3(1)+10(6)=63 1 7 * 6 2 row2column1= 1(1)+7(6)=43 9 0 row3column1= 9(1)+0(6)=9 row1column2= 3(8)+10(2)=44 row2column2= 1(8)+7(2)=22 row3column2= 9(8)+0(2)=72 Answer = 63 44 43 22 9 72 Exponential Function: A nuclear power plant worker has a starting salary of $80,000, this will increase 5% a year. Write an equation that represents this situation. How much will this person make in 10 years? a) y= 80,000(1+.05)* ---> y= 80,000(1.05)* b) y= 80,000(1.05)^10 = $130,311.6 Elective Problem: A car salesman makes $15,000 a year, for every sale he makes he earns an extra $15o. Write an equation that represents this situation.
( 9 marks ) (b) Calculate the total working hours. ( 1 mark ) Question 2 ( 10 marks ) Complete the following transportation table for initial solution, using | To | D | E | F | Supply | From | | | | | | A | | | 9 | | 5 | | 3 | 400 | B | | | 7 | | 3 | | 7 | 300 | C | | | 10 | | 2 | | 8 | 200 | Demand | | 450 | | 220 | | 230 | | 900 | (a) Northwest Corner Method ( 4.5 marks ) (b) Least Cost Method ( 4.5 marks ) (c) Which initial solution produces the lowest total cost ? ( 1 mark ) Question 3 ( 10 marks ) Suki Corp specializes in manufacturing computer tables. It is considering of building a new factory to manufacture the tables. The size of the factory is either large, medium and small.
c. What would be the effect on the optimal solution if the cost of operating mill 1 increased from $6,000 to $7,500 per day? d. What would be the effect on the optimal solution obtained in part c, if the company could supply only 10 tons of high-grade aluminum? e. In the original model (the one you formulated in part a): what is the shadow price for each of the three aluminum grades? f. In the original model: what is the sensitivity range for the objective function coefficients? Question 2 (16 points) Gilbert Moss and Angela Pasaic spent several summers during their college years working at archeological sites.
The equal probability of the copier breaking down before or after is the average time between breakdowns. So z^2/36 = 1/2. Solving gives z = 4.243 weeks. The uniform distribution for the number of copies sold per day, standard number of copies sold will be the average of the high and low estimates, which is 5000 copies per day. At 10 cents each, the expected revenue of $500 per day, and the amount will be lost while the copier is broken.
I then multiplied this number by 35,040 to find the amount of water lost in a whole year and I got 12,591.73. I’m assuming the water that enters the water heater is 40-degrees F and it leaves the heater at 120-degrees F. It takes 1 BTU to raise the temperature of 1 pound of water 1-degree