A gardener plans the lengths (in metres) of two straight flower beds along the – and…
MATHEMATICS · Multi-part · CBSE · Mathematics · Linear Programming · Linear Programming
Problem
A gardener plans the lengths (in metres) of two straight flower beds along the x– and y–axes from the origin such that the total length satisfies 2x+3y≤18. Only points in the first quadrant are relevant for planting.
(i) Write down the equation of the boundary line and find its x– and y–intercepts.
(ii) Draw the boundary line on graph paper, indicating clearly whether it is solid or dotted.
(iii) Using an appropriate test point, shade the region that represents all possible pairs (x,y) of flower–bed lengths that meet the gardener’s requirement within the first quadrant.
(iv) List all ordered pairs of non-negative integers (x,y) that satisfy the inequality and lie on the grid points of your graph.