Question:

The following table is a transportation matrix showing the cost ($) per unit of shipping from Plant i to Distributor j. The objective is to minimize shipping costs while meeting the demand placed by each Distributor. There is no shipment between Plant 2 and Distributor 3.

Distributor 1 Distributor 2 Distributor 3 Supply

Plant 1. 9 22. 24. 430

Plant 2. 14. 10 ..... 360

Plant 3. 18. 12. 13 220

Demand 400 390 190. ---

Let xij = number units shipped from Plant i to Distributor j

Solve the transportation problem and use the result to fill the boxes below.

All answers are equally weighted.

a) At optimal solution:

x11=

x12=

x13=

x21=

x22=

x23=

x31=

x32=

x33=

Minimum Cost = $

b) At optimal solution, how much unused capacity is available at each Plant?

Slack at Plant 1 = units

Slack at Plant 2 = units

Slack at Plant 3 = units

The Birth-and-Death Process Consider the birth-and-death process with the following mean rates. The birth rates are 20= 2, 21= 3, 12=2, 23=1, and an = 0 for n > 3. The death rates are ul= 3, 12=4, (3= 1, and un = 2 for n > 4. A. Construct the rate diagram for this birth-and-death process. B. Develop the balance equations. C. Solve these equations to find the steady-state probability distribution PO, P1, D. Use the general formulas for the birth-and-death process to calculate PO, P1, Also calculate L , La, W , and Wa.Eonsider the birth-and-dealh process with the following mean rates. The birth rates are in: 2, 11: 3, In: 2,. 1g: 1, and}. =forn: 3.11142de rates are [11:3, [11:4, |.J.a= 1, and p." =2forn :- 4. a] Construct the rate diagram for this birthanddeath process. B] 1 Construct the rate diagram for this birthand death process. cl] Solve these equations to nd the stead ystate probability distribution PD, P1 ..... d] Use the general formulas for the birthanddeath process to calculate PU, P1 ..... Also calculate L , Lq , W, and No. Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The amount of snowfall in December in City A b. The time it takes to fly from City A to City B c. The response to the survey question "Did you smoke in the last week?" d. The number of statistics students now reading a book e. The amount of rain in City B during April f. The weight of a T-bone steak a. Is the amount of snowfall in December in City A a discrete random variable, a continuous random variable, or not a random variable? O A. It is a continuous random variable. O B. It is a discrete random variable. O C. It is not a random variable. b. Is the time it takes to fly from City A to City B a discrete random variable, a continuous random variable, or not a random variable? O A. It is a discrete random variable. O B. It is a continuous random variable. O C. It is not a random variable C. Is the response to the survey question "Did you smoke in the last week?" a discrete random variable, a continuous random variable, or not a random O A. It is a continuous random variable. O B. It is a discrete random variable. O C. It is not a random variable. d. Is the number of statistics students now reading a book a discrete random variable, a continuous random variable, or not a random variable? Click to select your answer.The density f (a ) = e (I-1)2/202 correspond to a V2TO X O exponential random variable O geometric random variable O standard normal random variable O Binomial random variable uniform continuous random variable O Bernoulli random variable O normal random variable