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:

Note* The price for the Brick candle is $10.00 with tax of 8.25% tax and without it %12.90 and the Egyptian candle is $14.00 with tax of 8.25% and without it $13.96

jjennylove
Nov 28, 2018

#1**+4 **

I am not sure I understand your question. Could you please elaborate more or give more information?

PartialMathematician
Nov 28, 2018

#3**+4 **

Also, you said, "Note* The price for the Brick candle is $10.00 with tax of 8.25% tax and without it %12.90 and the Egyptian candle is $14.00 with tax of 8.25% and without it $13.96." Is "without thing" the price or percent? I think you meant $12.90.

Let's assume you meant, "Note* The price for the Brick candle is $10.00 with tax of 8.25% tax and without it $12.90." Without the 8.25% tax, the price is $12.90, which is more expensive than the price with tax, $10.

PartialMathematician
Nov 28, 2018

#4**+4 **

That's ok, I'll get someone else to answer this question if you need help.

PartialMathematician
Nov 28, 2018

#5**+1 **

Maybe this will help , this is the question before it with the answer

Youâ€™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:

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. Where I live it 8.25%, so adjusted for an even dollar value. A retail price of $9.87 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 $13.96 so tax brings it to $14

jjennylove
Nov 28, 2018

#6**+4 **

Yea, this makes more sense because we know that a candle costs $1.60 each. We also know the the cost of the brick.

PartialMathematician
Nov 28, 2018

#7**0 **

They part im confused at is how would i write a linear program model and constraits with those values as well as how i would be able to graph the feasible region and maxiumum and minium profits

jjennylove
Nov 28, 2018

#8**+3 **

The problem does not tell us how much time or how many candles we can make, so I guess theoretically the maximum is \(\infty\) and the minimum is 0.

If there was a restraint of time or whatever, for the number of candles \(n\), the maximum profit is: {selling price} - {making/producing price} * n. The minimum is $0, just don't make any candles.

PartialMathematician
Nov 28, 2018

#9**0 **

In the question it asks for a accetable range so there has to be one I believe, i have to make candels

jjennylove
Nov 28, 2018

#11**+1 **

let's go w/retail prices of

$9.25 for the brick, with a profit of $3.17

$13.00 for the egyptian with a profit of $4.40

Let's say management says you get to spend $1000 on this promotion

we have non-negative variables b and e which are the number of bricks and egyptians you want to produce for the promotion.

we want to produce at least say 10 each because we want to see how they'll sell.

We have the following constraints

\(b \geq 10\\ e \geq 10\\ 6.08 b + 8.60e \leq 1000 \\ \text{and we want to maximize the profit }\\ p=3.17b + 4.40e\)

Rom
Nov 28, 2018

#14**0 **

i figured out where it came from , when i got to plot the constraints what if it is a long decimal like the constraint 6.08x+8.06y<1000 ?i got the point (10,116.526) how would I then solve it to find the maxiumum ? do I simplify 116.526?

jjennylove
Nov 28, 2018