Question

. The specification for Fixit engine oil is that the specific gravity (SG) is at least 0.88, the viscosity is at most 32, and the sulphur content does not exceed 0.35%. A manager intends blending x barrels of Oil X and y barrels of Oil Y with 100 barrels of Oil Z that is in stock to produce a maximum volume of Fixit, subject to meeting the specifications. The relevant properties of Oil X and Oil Y and Oil Z are given in Table 1.

Oil SG viscosity sulphur % availability

X 0.92 44 0.45 unlimited  

Y 0.86 40 0.25 90

Z 0.89 20 0.30 100

(a) The viscosity requirement is (44x + 40y + 20 × 100 /x + y + 100) ? 32. (You can understand this via a simple example: if you combine two barrels of Oil X, then the viscosity must remain the same. We get this by adding the viscosity of each barrel and then dividing by the number of barrels, i.e. (44 + 44)/(1 + 1) = 44.) Show that the inequality above be simplified to 3x + 2y ? 300.

(b) In the same way find expressions for the SG and sulphur requirements and simplify them.

(c) Express the other constraints on x and y as inequalities.

(d) Sketch the feasible region, and label each vertex with its coordinates.

Answer 1