Linear Programming problem

I have a linear programing problem but I am not sure where to start.

An artist is creating a mosaic that cannot be larger than the space allotted which is 4 ft tall and 6 ft wide. The mosaic must be at least 3 ft tall and 5 ft wide. The tiles come in two sizes: Smaller tiles are 4 in tall and 4 in wide, the larger are 6 in tall and 12 in wide. If the small tiles cost 3.50 and the larger tiles cost 4.50 each, how many of each should be used to minimize the cost? What is the minimum cost?

It says the solution must include: Objective function, constraints (inequalities) and then a graph of the constraints.

What do I need to set up or is there anything I can read up on, because when I was reading up on constraints and stuff it still didn't really make sense.

Re: Linear Programming problem

Quote:

Originally Posted by

**Rbai76** I have a linear programing problem but I am not sure where to start.

An artist is creating a mosaic that cannot be larger than the space allotted which is 4 ft tall and 6 ft wide. The mosaic must be at least 3 ft tall and 5 ft wide. The tiles come in two sizes: Smaller tiles are 4 in tall and 4 in wide, the larger are 6 in tall and 12 in wide. If the small tiles cost 3.50 and the larger tiles cost 4.50 each, how many of each should be used to minimize the cost? What is the minimum cost?

It says the solution must include: Objective function, constraints (inequalities) and then a graph of the constraints.

What do I need to set up or is there anything I can read up on, because when I was reading up on constraints and stuff it still didn't really make sense.

It has told you what you need, you need to state the objective function, the constrants and then graph them and solve the problem graphically.

The objective function is the function you want to maximise or minimise... In this case, you wish to minimise the cost.

If you call s the number of small tiles and l the number of larger tiles, since you know small tiles cost $3.50 each, and larger tiles cost $4.50 each, then the cost function is

$\displaystyle \displaystyle \begin{align*} C = 3.5s + 4.5l \end{align*} $

Now what are your constraints?

Re: Linear Programming problem

Quote:

Originally Posted by

**Prove It** It has told you what you need, you need to state the objective function, the constrants and then graph them and solve the problem graphically.

The objective function is the function you want to maximise or minimise... In this case, you wish to minimise the cost.

If you call s the number of small tiles and l the number of larger tiles, since you know small tiles cost $3.50 each, and larger tiles cost $4.50 each, then the cost function is

$\displaystyle \displaystyle \begin{align*} C = 3.5s + 4.5l \end{align*} $

Now what are your constraints?

Wouldn't the constraints be that the mosaic has to be at least 3ft tall and 5ft wide?

You would need 2 for the height and 2 for the width.

I just don't know what you are supposed to fill into the matricies

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