please help Me! I have been looking at this for 3 hours. Please answer!!10 points and possibly another 40!?
You can answer number two for an extra 40 points!!!! How i am going to give 40 points is by giving you a 4 links in best answer and you answer a silly question i posted and i will appoint you best answer. PLEASE HELP ME!!!! I AM LOST!!!! This is not homework.
1. It’s time to lock down the design details for the redesigned Brick and Egyptian candles. Because of manufacturing constraints, the base length for each candle has to be at lease 2 centimenters, but it can be no more than 10 centimeters. Make a recommendation for the base dimensions of each candle. Tell how you determined you base dimensions. Your reasoning does not have to be math related.
2. You’re instructed to prepare for a promotional candle sale you will use to test the popularity of the two redesigned candles. Wicks, labor, adn other costts add about .60 to the cost each candle.
Suggest a retail price for each candle that will cover costs adn allow for some profit. Tell how you determine these prices. Your reasoning doesn’t have to be all math related, but should include specific values derived for your calculations.
HERE ARE SOME HELPFUL THINGS MY MOM GAVE ME.
Determining cost of WAX: The same wax will be used to make each candle, and it costs 3/4 of a penny per cubic centimeter.
$.0075 times each cubic cm = cost OR $.0075 times volume = cost.
Find the cost for the dimensions ‘you choose.’
NOTE: there are additional costs as well for wick, labor, etc. Read the directions carefully to find these numbers.
Goal is to make a profit without the cost being so high that no one wants to buy it.
Make sure all answers include math calculations and detailed explanations of why you are making that decision.
You can answer number two for an extra 40 points!!!! How i am going to give 40 points is by giving you a 4 links in best answer and you answer a silly question i posted and i will appoint you best answer. PLEASE HELP ME!!!! I AM LOST!!!!
You offer is very tempting. But I won’t give you one solution. I’ll give you a range of solutions and you’ll choose whatever fits your problem best.
First of all you did not mention what shape must the candle have, but because you said BASE I’m thinking a right prism (in particular a cube, when all 12 sides are equal) OR a pyramid OR a right cylinder. The volume of a shape is [area_of_base]*[height] for the prism and cylinder , AND for the pyramid is [1/3]*[area_of_base]*[height]
THE SMALLEST FORMS:
- smallest prism —> the cube with all sides 2 ==> the volume is 2*2*2 = 8 cm^3
- smallest pyramid number one —> the pyramid with base sides 2 and the height also 2 ==> the volume is (1/3)*2*2*2 = 8/3 cm^3
- smallest pyramid number two —> the pyramid with base sides 2 and the lateral sides also 2 ==> the radius of the base is sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 – [base_radius]^2 = 2^2 – sqrt(2)^2 = 4 – 2 = 2 ==> pyramid_height = sqrt(2) ==> the volume is (1/3)*2*2*sqrt(2) = 4*sqrt(2)/3 cm^3
- smallest cylinder –> the cylinder of diameter 2 and height also 2 ==> the radius is diameter/2 = 2/2 = 1 ==> the volume is pi*(radius^2)*height = pi*(1^2)*2 = pi*1*2 = 2*pi cm^3
The lesser volume is the volume of the smallest pyramid number two. ==> it’s wax cost is approximately 0.0075 * 4 * 1.42 / 3 $ per candle = 0.014 $ per candle ==> the total cost per candle is approximately 0.014 + 1.6 = 1.614 $ per candle.
THE BIGGEST FORMS:
- biggest prism —> the cube with all sides 10 ==> the volume is 10*10*10 = 1000 cm^3
- biggest pyramid number one —> the pyramid with base sides 10 and the height also 10 ==> the volume is (1/3)*10*10*10 = 1000/3 cm^3
- biggest pyramid number two —> the pyramid with base sides 10 and the lateral sides also 10 ==> the radius of the base is 5*sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 – [base_radius]^2 = 10^2 – [5*sqrt(2)]^2 = 100 – 50 = 50 ==> pyramid_height = 5*sqrt(2) ==> the volume is (1/3)*10*10*5*sqrt(2) = 500*sqrt(2)/3 cm^3
- biggest cylinder –> the cylinder of diameter 10 and height also 10 ==> the radius is diameter/2 = 10/2 = 5 ==> the volume is pi*(radius^2)*height = pi*(5^2)*10 = pi*25*10 = 250*pi cm^3
The bigger volume is the volume of the biggest prism (the side-10 cube). ==> it’s wax cost is 0.0075 * 1000 $ per candle = 7.5 $ per candle ==> the total cost per candle is 7.5 + 1.6 = 9.1 $ per candle
The range of the cost is the interval [1.614 ; 9.1]. Depending on other prices on the market, you greed, and other factors you will put a profit margin: maybe 20% of the cost ; maybe a fixed margin like 5$. So the price per candle will be the cost per candle plus the profit margin per candle.
If I were to choose the base length I would have to say 6 because it is the arithmetic mean between 2 and 10: (2+10)/2 = 12/2 = 6. 2cm is too small, and 10cm is too big.
Also if you start with a rectangle of length 10 and width 2 and you have to find the rectangle with the largest area by being allowed to increase the width and decrease the width with the same quantity you get this:
Area of the new rectangle is (10-x)(2+x) = -x^2 + 8x + 20 = -x^2 + 8x -16 + 36 = -(x^2 – 2*x*4 + 4^2) + 36 = -(x-4)^2 + 36 = 36 – (x-4)^2 which has the maximum value of 36 because out of 36 you subtract a positive value. You get the maximum when (x-4)^2 = 0 ==> x-4=0 ==> x=4
The new length is 10-4=6 and the new width is 2+4=6.
Next I would choose the height of the prism (I like prisms
) to be [the_golden_ratio]*[base_side] which is approximately 1.618 * 6 = 9.708 which I would round up to 10. ==> The volume would be 6*6*10 = 360 cm^3. ==> the cost would be 0.0075*360 + 1.6 = 2.7 + 1.6 = 4.3 $ per candle. And because my candle is so perfect I’d put the profit margin to be 5.69 $ per candle so I can proudly show it in the store with the price of 4.3 + 5.69 = 9.99 $ 
Hope some of this will be of use!
Best regards!