1.13: Linear Programming on a Graph

4PM1/2R/June/2019 — Question 5 · 7 marks

1.13 diagram 1
(a) On the grid provided, draw the graphs of the lines with equations
2x+3y=24,y=2x,3y=2x−12.2x+3y=24, \qquad y=2x, \qquad 3y=2x-12.
(3)
(b) Show, by shading on the grid, the region R\displaystyle R defined by the inequalities
2x+3y⩽24,y⩽2x,3y⩾2x−12,y⩾0.2x+3y\leqslant24, \qquad y\leqslant2x, \qquad 3y\geqslant2x-12, \qquad y\geqslant0.
(1)
For all points in R\displaystyle R, with coordinates (x,y)\displaystyle (x,y),
F=2x+5y.F=2x+5y.
(c) Find the greatest value of F\displaystyle F.
(3)