A students’ committee plans to sell notebooks and pens to raise funds
MATHEMATICS · Multi-part · CBSE · Mathematics · Linear Programming · Linear Programming
Problem
A students’ committee plans to sell notebooks and pens to raise funds. Let x denote the number of notebooks and y denote the number of pens to be sold. The following requirements must be met:
• Each notebook uses 2 units of paper and each pen uses 1 unit of paper. The total amount of paper available is at most 40 units.
• At least 10 items in total must be sold.
• The committee cannot sell a negative quantity of any item.
Answer the following.
(i) Translate the above information into a system of linear inequalities in the variables x and y.
(ii) Draw the graphs of all boundary lines on the same set of axes and shade the feasible region that meets all the constraints.
(iii) List all the vertices of the feasible region found in part (ii).
(iv) Using your graph, determine the maximum possible number of notebooks that can be sold while still satisfying all the constraints. Justify your answer.