Senior 4 • Linear Programming • Showcase mission

The Fundraiser Production Plan

The school enterprise club has limited flour and oven time. Choose the production plan that earns the greatest profit without breaking either limit.

⏱ 65–80 minutes✎ Pencil and paper★ Explain every answer

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YOUR MISSION PROGRESS • 0 OF 15 PRACTICE QUESTIONS SOLVED0%

The situation

There are many possible plans—but only one best corner.

The club can bake banana loaves and mandazi trays. One loaf uses 2 flour units and 1 oven unit. One mandazi tray uses 1 flour unit and 2 oven units. Only 12 flour units and 12 oven units are available. Profit is UGX 6,000 per loaf and UGX 5,000 per tray.

⚠ THE PROBLEM YOU MUST SOLVE

How many loaves and mandazi trays should the club make for maximum profit?

Your job: define the variables, write the constraints, identify the feasible corner points, test the profit at each corner, and recommend the best plan.

Foundation • A constraint is a limit

The plan must satisfy every condition at once.

Let x be banana loaves and y be mandazi trays. A feasible plan uses no more flour or oven time than the club has. Linear programming compares all feasible choices efficiently by testing the corner points.

FLOUR LIMIT

2x + y ≤ 12

Each loaf uses 2 flour units and each tray uses 1. The total cannot exceed 12.

OVEN LIMIT

x + 2y ≤ 12

Each loaf uses 1 oven unit and each tray uses 2. This total also cannot exceed 12.

PROFIT FUNCTION

P = 6,000x + 5,000y

Use this rule to compare the profit earned at every feasible corner.

Worked example • Follow the reasoning

Test the four feasible corner points.

The boundary lines meet the axes and each other at (0,0), (6,0), (4,4) and (0,6). Evaluate P at each point.

AXIS CORNERSP(0,0)=0; P(6,0)=36,000

Six loaves use all 12 flour units.

INTERSECTIONP(4,4)=24,000+20,000=44,000

This plan uses exactly 12 flour units and 12 oven units.

FINAL CORNERP(0,6)=30,000

The largest tested profit is UGX 44,000 at (4,4).

QUICK CHECK 1

Which inequality represents the flour limit?

QUICK CHECK 2

Is the plan (3,3) feasible?

QUICK CHECK 3

What profit is earned at (4,4)?

QUICK CHECK 4

Which conditions stop the club planning negative products?

QUICK CHECK 5

Is the plan (5,2) feasible?

QUICK CHECK 6

Why is the plan (5,4) not feasible?

QUICK CHECK 7

What is P at the corner (6,0)?

QUICK CHECK 8

What is P at the corner (0,6)?

QUICK CHECK 9

Where do 2x+y=12 and x+2y=12 meet?

QUICK CHECK 10

Which expression is the objective function?

QUICK CHECK 11

For 2x+y≤12, does the origin belong to the feasible side?

QUICK CHECK 12

Why should x and y usually be whole numbers here?

QUICK CHECK 13

At (3,3), how many flour units remain unused?

QUICK CHECK 14

Which corner earns more: (6,0) or (0,6)?

QUICK CHECK 15

If profit changed to UGX 4,000 per loaf and UGX 7,000 per tray, which listed corner would be best?

Final scenario challenge

Which production plan should the club approve?

Every option below is a corner point. Choose the plan with the greatest verified profit.

Explain your thinking

Why is the most profitable plan found by checking feasible corner points?

Write two or three sentences. Use the mathematical steps from the mission as evidence—not only the final answer.

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Workbook and teaching support

Continue on paper, teach it in class, or send the guided activity home.

STUDENT PDF

Mission Workbook

Foundation notes, guided practice, final scenario and reflection.

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Teaching Guide

Lesson flow, support prompts, misconceptions and complete answers.

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Senior 4 SHOWCASE MISSION

You made the mathematics visible.

A strong answer does not guess. It represents, calculates and explains.

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