Inequalities on a number line, graphing inequalities in two variables, the feasible region, and using the objective function to maximise or minimise.
5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.
A baker has limited flour and time. A farmer has limited land and money. Linear programming finds the best plan — and it only needs a graph and a calculator.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Find the vertex that gives the maximum profit.
Copy these into your notebook in your own words — that is how they stick.
Open circle for < >; closed for ≤ ≥.
Replace the inequality by =; solid for ≤ ≥, dashed for < >.
Substitute (0, 0) (if not on the line) to decide which side to shade.
Follow the question: shade the required region OR the unwanted region.
Satisfies ALL constraints; its corners are the vertices.
Solve pairs of boundary equations simultaneously.
Evaluate at each vertex; the largest (or smallest) gives the optimum.
Check the optimum is sensible (whole numbers, non-negative).
3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Mathematics Arcade.
8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.
Write full answers, then reveal the mark scheme and tick the points you earned (19 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [10 marks]
A baker makes x cakes and y pies in a day. He makes no more than 8 items in total (x + y ≤ 8) and the ovens allow 2x + y ≤ 12. Also x ≥ 0 and y ≥ 0.
(a) Draw the lines x + y = 8 and 2x + y = 12 for x from 0 to 8, and shade the UNWANTED regions so the feasible region R is left clear. (Check: lines through (0, 8), (8, 0) and (0, 12), (6, 0); R is the quadrilateral O(0, 0), (6, 0), (4, 4), (0, 8).) [4]
(b) The profit is P = 5x + 4y dollars. Find the coordinates of each vertex of R. [3]
(c) Hence find the maximum profit and the number of cakes and pies that gives it. [3]
Question 2 [9 marks]
Lisa has $56 to buy red balloons (x) and green balloons (y) for a party. Red balloons cost $0.75 each and green balloons cost $0.50 each. She buys no more than 70 balloons, at least 15 red balloons, and more green balloons than red balloons.
(a) Write four inequalities in x and y to represent the information. [4]
(b) Show that the point (20, 40) satisfies all four inequalities. [3]
(c) Is (30, 35) a possible purchase? Explain. [2]
Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.