D1 January 2009 Q7

EdexcelOld spec12 marksLinear Programming

7. A linear programming problem is modelled by the following constraints

\[\begin{aligned} 8x + 3y &\leqslant 480\\ 8x + 7y &\geqslant 560\\ y &\geqslant 4x\\ x, y &\geqslant 0\end{aligned}\]
(a) Use the grid provided in your answer book to represent these inequalities graphically. Hence determine the feasible region and label it R. (6)

The objective function, \(F\), is given by

\[F = 3x + y\]
(b) Making your method clear, determine
(i) the minimum value of the function \(F\) and the coordinates of the optimal point,
(ii) the maximum value of the function \(F\) and the coordinates of the optimal point. (6)
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