Question

An oil company required 12000, 20000 and 15000 barrels of high-grade, medium grade and low grade oil, respectively. Refinery A produces 100, 300 and 200 barrels per day of high-grade, medium-grade and low-grade oil, respectively, while refinery B produces 200, 400 and 100 barrels per day of high-grade, medium-grade and low-grade oil, respectively. If refinery A costs ? 400 per day and refinery B costs ? 300 per day to operate, then the days should each be run to minimize costs while satisfying requirements are

• A. 30, 60
• B. 60, 30
• C. 40, 60
• D. 60, 40

Answer 1

Answer: (B)

60, 30

Answer 2

The given data may be put in the following tabular form Suppose refineries A and B should run for x and y days respectively to minimize the total cost. The mathematical form of the above is Minimize $Z = 400x + 300y$ Subject to $100x + 200y \ge 12000$ $300x + 400y \ge 20000$ $200x + 100y \ge 15000$ and $x, y \ge 0$ The feasible region of the above LPP is represented by the shaded region in the given figure. The corner points of the feasible region are $A_2(120, 0), P(60, 30)$ and $B_3(0, 1 50)$. The value of the objective function at these points are given in the following table Clearly, $Z$ is minimum when $x = 60, y = 30.$ Hence, the machine $A$ should run for $60$ days and the machine$B$ should run for $30$ days to minimize the cost while satisfying the constraints.