PLEASE DO NOT HANDWRITE THE ANSWERS, AND ALL THE QUESTIONS MUST BE ANSWERED PLEASE!

( 1 ) a. A firm makes paper at three locations: Seattle (Washington), Kalamazoo (Michigan), and Boise (Idaho). The product is needed in four locations: New York, Chicago, Houston, and Los Angeles. The demand in tons, the capacities in tons, and the cost of shipping one ton of paper from each source to each demand center are given below:

                demand               500         400         450         600

capacity                              New York            Chicago Houston              Los Angeles

400         Seattle 250         150         200         100

800         Kalamazoo          150         75           250         300

1200       Boise     200         180         220         90

For example, the capacity of the plant in Seattle is 400 tons; the demand at Houston is 450 tons; and the cost of shipping one ton of paper from Seattle to New York is $250.

Find the least cost of transporting the material. (All assumptions of the transportation model holds, such as the linearity of the cost of shipment)

b. Consider the following game: you pay $4 to play, and then you roll a die (which is fair and unbiased). You get double of the number you roll - i.e. if you rolled 4, you get $8.

Find the expected value of this game. (Find the expected value of your payoff, and then subtract the $4 you paid to play the game).

c. A vendor has to decide how many magazines to stock for the day. The demand distribution is

magazines demanded   0              1              2              3              4

probability         0.2          0.25        0.3          0.15        0.1

The cost of a magazine to the vendor is $1; it can be sold at $3; but if it remains unsold at the end of the day, the magazine has no value at all.

So for example, if the vendor stocks 2 magazines, then the profit would be -2, +1, +4, +4, and +4 with corresponding probabilities 0.2, 0.25, 0.3, 0.15, and 0.1. The expected profit is $2.05.

How many magazines should be stocked to maximize the expected profit? (The decision alternatives are 0, 1, 2, 3, or 4; the states of nature are the possible demands)

d. Generate a random number between zero and ten (hint: "=RAND()*10")

Find its square. Repeat that for one hundred values (copy the line 99 times). Find the average value of the squares.

e. What is the expected (average) value of the square of the roll of a die?

We know that the average value of the roll of a die is 3.5 (it takes values 1, 2, 3, 4, 5, and 6 with equal probability). So would the average of the square of the roll of a die be equal to square of 3.5? We can find that out through simulation.

In Excel, roll a fair die (=trunc(rand()*6)+1), and find the square of that value (i.e. if you roll 5, its)