Linear Programming Problems from Words

Name: Linear Programming Problems from Words
Author: StemPy Lab

A workshop, a canteen and a delivery van all face the same question: what is the best plan with limited resources? Turn the story into variables, an objective and constraints, draw the region, find the best corner and say what it means in the units of the problem. Manufacturing, diet and transport problems, in the style of the board and CUET papers.

3 lessons, about 1 h 20 min3 simulations10 problems3 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
Manufacturing problems
A manufacturing problem asks how many of two products to make so that the profit is greatest, when machine hours or materials are limited. To solve it, name the two quantities as $x$ and $y$ , write the profit as the objective function, turn each limit into an inequality, and add $x \ge 0$ and $y \ge 0$ . Then draw the region, find the corners, and pick the best. Finish with a sentence that gives the plan and the profit with their units.
1 simulation1 practice question1 Python program3 problems1 Python lab
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Lesson 2about 25 min
Diet and mixing problems
A diet or mixing problem asks for the cheapest mix of two foods that still meets minimum needs. The needs give inequalities with $\ge$ , so the feasible region is unbounded, and the objective is a cost to be minimised. Find the corners, work out the cost at each, and take the smallest. Confirm that it is a true minimum with the half-plane test, and say the answer in kilograms and rupees.
1 simulation1 practice question1 Python program3 problems
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Lesson 3about 30 min
Transport and allocation problems
A transport problem sends goods from two depots to two shops at the least cost. It has four shipments, but the shops' needs fix two of them once the other two are chosen, so only $x$ and $y$ are unknown. The shipments that are left must not be negative, and each depot must not send more than it holds. This gives a region with several corners. Allocation problems, such as investments, follow the same steps. When whole numbers are needed, check the plans near the best corner.
1 simulation1 practice question1 Python program4 problems1 Python lab1 question set1 note
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Linear Programming: Chapter Test

Board exam format20 questions · 30 min

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Linear Programming Problems from Words

Course outline (3 lessons)

Manufacturing problems

Diet and mixing problems

Transport and allocation problems

Test Your Learning

Your teacher

Discussion (0)