You are finalizing your notes and graphs for your meeting with the executives of BeeSwaks. You must be prepared to make a recommendation for the base dimensions, suggest retail prices, and discuss possible profits from a preliminary candle sale that you set up for a marketing campaign.

In case you need the equation for the Brick candle is x^{3}-x^{2 }and the the equation for the Egyptian candle is 7x^{2} .

Answer the questions below.

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 least 2 cm and can be no more than 10 cm. Make a recommendation for the base dimensions of each candle. Explain how you determined your base dimensions. Your reasoning does not have to be all math related.

Answer:

You’re instructed to prepare for a promotional candle sale you will use to test the popularity of the two redesigned candles. Wicks, labor, and other costs add about $1.60 to the cost of each candle.

Suggest a retail price for each candle that will cover costs and allow for some profit. Explain how you determined these prices. Your reasoning does not have to be all math related, but it should include specific values derived from your calculations.

Answer:

You ask the production team to make some candles for the sale. The team is not sure how many they can produce in your short time frame, so they ask for an acceptable range for how many of each candle they should make.

Use your costs and recommended retail prices to write a linear programming model to show the BeeSwaks executives possible profits for selling certain numbers of each type of candle during this promotion. Decide on the constraints for the numbers of candles made for the sale and explain your reasoning for these constraints. Graph the feasible region and find maximum and minimum profits.

Answer:

jjennylove
Nov 11, 2018

#1**+2 **

From the last problem we saw that a point of interest was a base of 8cm with a volume of 448 cm^{3}

That's where the volumes of the two candle types are equal and thus of equal materials cost to make.

Below this size the brick was cheaper, above it the egyptian is cheaper.

If I had to design a candle I think the following things would be factors

a) taller and slimmer is probably more attractive

b) we want the brick stand securely on the table without tipping so a bigger base is better

c) the egyptian has no tipping problem

So I'd make the brick as big as possible before the volumes became the same, i.e. 8cm.

Larger than that I'd make egyptians and I guess we'd just make them as large as possible i.e. 10cm

cost of the brick is $4.48 + $1.60 = $6.08

50% markup is typical on things like decorative candles so a profit of $3.04

for a total retail price of $9.12

I'd then figure the sales tax for my area. Here it's 7.5%. And I'd adjust it for an even dollar value.

A retail price of $9.30 comes to $10 with tax

cost of the egyptian is $7.00 + $1.60 = 8.60$

markup of $4.30 gives a retail price of $12.90

same story with the sales tax. I'd price it at $13.02 so tax brings it to $14

leaving the last bit for you

Rom
Nov 11, 2018

#1**+2 **

Best Answer

From the last problem we saw that a point of interest was a base of 8cm with a volume of 448 cm^{3}

That's where the volumes of the two candle types are equal and thus of equal materials cost to make.

Below this size the brick was cheaper, above it the egyptian is cheaper.

If I had to design a candle I think the following things would be factors

a) taller and slimmer is probably more attractive

b) we want the brick stand securely on the table without tipping so a bigger base is better

c) the egyptian has no tipping problem

So I'd make the brick as big as possible before the volumes became the same, i.e. 8cm.

Larger than that I'd make egyptians and I guess we'd just make them as large as possible i.e. 10cm

cost of the brick is $4.48 + $1.60 = $6.08

50% markup is typical on things like decorative candles so a profit of $3.04

for a total retail price of $9.12

I'd then figure the sales tax for my area. Here it's 7.5%. And I'd adjust it for an even dollar value.

A retail price of $9.30 comes to $10 with tax

cost of the egyptian is $7.00 + $1.60 = 8.60$

markup of $4.30 gives a retail price of $12.90

same story with the sales tax. I'd price it at $13.02 so tax brings it to $14

leaving the last bit for you

Rom
Nov 11, 2018

#2**+1 **

Thank you so much for your information I will use this as a reference when building my own product .

For the last bit,is there anyway you would be able to help me , how would I find the constraints and model the programming ?you dont have to give me the exact answer but just a tip on how I would ? I am sorry I am confused with these .

jjennylove
Nov 11, 2018