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```1) Turkmen Oil Ltd. is an oil conglomerate that has a network of pipelines and intermediate  oil storage facilities connecting oil fields in Baku, Azerbaijan and to the newly built oil refinery in Adana, Turkey. Crude oil can be pumped from the oil field to any of the intermediate storage facilities A, B, and C in Azerbaijan. The maximum flow capacity from the oil field to intermediate storage facilities A, B, and C is 20, 15 and 22 thousand barrels oils per day respectively. Oil is pumped from these three major intermediate storage facilities to other intermediate processing facilities in Turkey labeled D, E, F, G and H. The oil finally pumped from these facilities (D, E, F, G and H) to the oil refinery in Adana for final processing. The pipeline branches comprising of this network and their respective flow capacities are given below.
a) Formulate the problem as a linear programming problem
b) Use Excel and determine the maximal flow of oil in thousands of barrels per day from oil
field to the oil refinery.
c) State the amount of flow in thousands of barrels on each branch.

2) There are three brands of hair colour available in the market, manufactured by prestigious
manufacturers. However, the association of hair colour manufacturers feels that the brand loyalty within this segment is not all that great. A market survey company was appointed to observe the brand switching probabilities of the consumers and the results are as tabulated in table.

(a) Develop the transition probability matrix.
(b) Calculate the market share for each of the brand after two rounds of purchases, excluding the present purchase.
(c) Calculate the market share for each brand in the long run.

3) A small paint company manufactures two types of paint, latex and enamel. In production, the
company uses 10 hours of labor to produce 100 gallons of latex and 15 hours of labor to produce 100
gallons of enamel. Without hiring outside help or requiring overtime, the company has 40 hours of
labor available each week. Furthermore, each paint generates a profit at the rate of \$1.00 per gallon.
The company has the following objectives listed in decreasing priority:
avoid the use of overtime
try to achieve a weekly profit of \$1000
produce at least 700 gallons of enamel paint each week
Develop GP and solve it through Excel.

4) The owner of a catering company wants to use exponential smoothing to forecast demand for thecatering service. These historical values reflect recent experience:

a) Use the data to develop a model. Choose between a smoothing constant of 0.1 to 0.9. Suggest the best smoothing constant. What is the demand forecast for the week 15 based on best smoothing constant.
b) For the above data, fit the regression equation and provide excel output and forecasted value for week 15 based on regression equation.

5) Bubblerware Industries Ltd. manufacture three rubber based products: Airtex (a spongy material), Extendex (Stretch material) and Resitex (hard material). All three products require same three chemical polymers and a base. The amount of each ingredient used per pound of final product is given
in Table below.

For the coming week, Bubblerware has a commitment to produce at least 1000 pound of Airtex, 500 pounds of Extendex and 400 pounds of Restex, but the company management knows it can sell more of each of these three products. Current inventories of the ingredients are 500 pounds of polymer A, 425 pounds of polymer B, 650 pounds of polymer C and 1100 pounds of base. Each pound of Airtex nets a
company a profit of \$7, each pound of Extendex a profit of \$7, and eaxh pound of Resitex a profit of \$6. As a manager of the production department, you need to determine an optimal production plan for this week. Attach all your Excel output.

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