(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

#56.) Someone makes necklaces and sells them for 10 dollars each. His average sales were 20 per day. When he raises the price to 11 dollars per day, the average sales drops 2.

a.)Find the demand function, assuming it is linear.

b.)If the material to make each necklace costs 6 dollars, what should the selling price be to maximize profit?

#14.)A rectangular container with an open top is to have a volume of 10m^3. The length of it's base is twice the width. Materials for the base cost 10$ per square meter. Material for the sides cost 6$ per meter. Find the cost of materials for the cheapest such container.

2. Relevant equations

3. The attempt at a solution

For #56 I have solved part a.) I found the demand function to be

[tex]y=-2x[/tex]

For part b. I am a bit confused.

It seems to me like I should just let x = (x-6), and then maximize that function? Is that the correct idea?

#14.)For this one I made a box and labeled it's dimensions:

[tex]h(w)(2w)[/tex]

Then I got thinking about it, and I don't know how to set this one up at all.

I worked out the following:

[tex]LWH = 10[/tex]

[tex]L = 2W[/tex]

[tex]2W^{2}H = 10[/tex]

Area for the sides is:

[tex]2(2WH)+2(HW)[/tex]

Area for the base is:

[tex]2W^{2}[/tex]

I just don't know how to relate all of these together? I think it's a similar style to the other problem I posted here, which is why I grouped them together. What is the next step to relate these functions to their appropriate costs so that I can maximize? For the container one, I thought I would just have to find the minimum surface area of the box that still had the volume of 10, but the two different costs ruined that idea for me.

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# Homework Help: 2 Optimization problems!

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