Linear Programming word problems

In summary, linear programming is a mathematical method used to find the optimal solution to a problem with multiple constraints. It has various real-world applications such as supply chain management, resource allocation, and production planning. To solve a linear programming problem, it must first be formulated as a mathematical model and then various methods can be used. Linear programming can only be used for problems with linear objective functions and constraints, while non-linear problems require other techniques. A feasible solution satisfies all the constraints, while an optimal solution is the most optimal among all feasible solutions.
  • #1
glaceau
1
0
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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  • #2
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?
 

FAQ: Linear Programming word problems

What is linear programming?

Linear programming is a mathematical method used to find the optimal solution to a problem with multiple constraints. It involves minimizing or maximizing a linear objective function, subject to linear constraints.

What are some common applications of linear programming?

Linear programming has various real-world applications, such as in supply chain management, resource allocation, production planning, and finance. It can also be used in agriculture, transportation, and telecommunications.

How is a linear programming problem solved?

A linear programming problem is solved by first formulating the problem as a mathematical model with an objective function and constraints. Then, various methods like the simplex method or the graphical method can be used to find the optimal solution.

Can linear programming be used for non-linear problems?

No, linear programming can only be used for problems with linear objective functions and constraints. Non-linear problems require other mathematical techniques such as non-linear programming.

What is the difference between a feasible solution and an optimal solution in linear programming?

A feasible solution is one that satisfies all the constraints of the problem, whereas an optimal solution is the most optimal or best solution among all feasible solutions. In other words, an optimal solution maximizes or minimizes the objective function, while also satisfying all the constraints.

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