Linear Programming word problems

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SUMMARY

The discussion centers on solving a linear programming problem for a small business that manufactures laptops and notepads. The constraints include a maximum of £1350 for labor costs and £1150 for material costs. Laptops require £50 in materials and labor, yielding a profit of £110 each, while notepads cost £25 in materials and £40 in labor, with a profit of £70 each. The objective is to determine the optimal number of laptops and notepads to produce monthly to maximize profit.

PREREQUISITES
  • Understanding of linear programming concepts
  • Familiarity with profit maximization techniques
  • Basic knowledge of constraints in optimization problems
  • Ability to formulate equations based on word problems
NEXT STEPS
  • Learn how to set up linear programming models using graphical methods
  • Study the Simplex method for solving linear programming problems
  • Explore software tools like Excel Solver for optimization tasks
  • Investigate real-world applications of linear programming in business
USEFUL FOR

Students, educators, and professionals in operations research, business management, and anyone interested in optimizing production processes for maximum profitability.

glaceau
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a small business makes laptops and notepads. In any given month labour costs must not exceed £1350 and material costs must be a maximum of £1150.

Relevant information:
Laptops cost £50 in materials to make and labour costs £50, they make £110 profit on each laptop.
notepads cost £25 in materials to make and labour costs £40, they make £70 profit on each notepad.

QUESTION: HOW MANY OF EACH TYPES OF COMPUTER SHOULD THE COMPANY AIM TO SELL EACH MONTH IN ORDER TO MAKE THE MAXIMUM PROFIT?

Thanks if anybody can answer this question!
 
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Hello and welcome to MHB, glaceau! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 

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