Three types of gasoline are manufactured by a company - Regular. Super, and Extr

Question

Three types of gasoline are manufactured by a company - Regular. Super, and Extra. Regular should have at least 11 percent additive 1 and 17 percent additive 2. Super should have at least 13 percent additive I and 22 percent additive 2. Extra should have at least 17 percent additive I and 19 percent additive 2. These are made by using two crudes - A and B. Crude A cost $28 per barrel and is 14 percent additive 1 and 18 percent additive 2. Crude B costs $30 per barrel and is 20 percent additive 1 and 24 percent additive 2. The demand for Regular is projected to be 1,000 barrels, while each of the others has a demand of 2,000 barrels. Formulate this as a linear programming problem to minimize cost while meeting all constraints. Formulate this problem A small software development project has four major activities. The times are estimated and provided in the table below. (a) What is the expected completion time for this project? (b) Draw the network and state the ES, EF, LS,LF, slack, in a Table. (c) State the critical path ? (d) What is the expected variance of the critical path? (e) List the non critical activities?

Explanation / Answer

Let the Additive A be x and Additive B be y Cost of Crude A = $ 28 (0.14x + 0.18y) = 3.92x + 5.04y Cost of Crude B = $ 30 (0.20x + 0.24y) = 6x + 7.2y Hence, Cost of Additives 1 and 2 equals = 9.92x + 12.24y To minimize cost, the objective fucntion Z = 9.92x + 12.24y Subject to, 0.11x + 0.17y 1000 (Regular Gasoline Constraint) 0.13x + 0.22y 2000 (Super Gasoline Constraint) 0.17x + 0.19y 2000 ( Extra Gasoline Constraint) x,y 0 (Non Negativity Constraint)

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