A2 Question 2

[Adi]

Hey FMH, I am currently working on a business maths assignment and because I haven't done any maths since high school in 2011 prior to undertaking this unit I am very much out of my depth. I am posting all of the questions on here individually and plan to work on them step by step on here so that you guys and gals can tell me if I am doing things right or not. Any hints on what rules need to be applied and what parts of the question mean in plain english would also be much appreciated. If it takes me a while to reply it will be because I am currently focused on a different question but rest assured I will come back to this question eventually and any help will be very much appreciated. You guys are the best, thanks so much.

 

[Otis]

... I am posting [my exercises] ... and plan to work on them step by step on here so that you guys and gals can tell me if I am doing things right or not.

... If it takes me a while ... I am currently focused on a different question but rest assured I will come back to this question eventually ...

We look forward to seeing your work so far, as well as any specific questions you may have about this exercise. Cheers

?

 

[Adi]

Thanks Otis. I think I know how to do part b already but I have no idea how to do part a. Its asking me to somehow use the first four functions to prove that pie(x,y) is the total profit function right?

 

[Harry_the_cat]

Revenue = Price x Quantity sold
So Total revenue = x*Price of A +y*Price of B
Profit = Total Revenue - Total Cost

 

[Adi]

Thanks Harry. Do I need to solve PA and PB to get the prices of the two goods?

 

[Adi]

Thanks Harry. Do I need to solve PA and PB to get the prices of the two goods?

never mind I worked out what you were saying. I have now worked out the TR equation with your help.

 

[Adi]

I've finished part B and gotten x=100, y=50. Now on to part c. I take it the constraint is x+y=60?

 

[Adi]

I've solved the Lagrange equation made by combining the profit equation with the constraint and got x=-878.0952, y=938.0953, λ=769.5238.

So for part d and I right in thinking that the lagrange multiplier value at the maximum point is f(-878.0952, 938.0953, 769.5238).

Then buy substituting these values for x and y into the profit function I get a maximum profit of -7224576.2793units. I think I must have done somthing wrong because I wouldnt have expedted the maximum profit to be negative. Can anybody help?

 

[Adi]

I've solved the Lagrange equation made by combining the profit equation with the constraint and got x=-878.0952, y=938.0953, λ=769.5238.

So for part d and I right in thinking that the lagrange multiplier value at the maximum point is f(-878.0952, 938.0953, 769.5238).

Then buy substituting these values for x and y into the profit function I get a maximum profit of -7224576.2793units. I think I must have done somthing wrong because I wouldnt have expedted the maximum profit to be negative. Can anybody help?

I think I must have incorrect values for x and y because the quantities shouldnt be negative either but I dont know where I went wrong

 

[Adi]

never mind I made some big mistakes before. I've solved it now