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

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 least 2 cm and can be no more than 10 cm. Make a recommendation for the base dimensions of each candle. Explain how it is determined your base dimensions. The reasoning does not have to be all math related.
2. It is instructed to prepare for a promotional candle sale will be used 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 it was determined these prices. The reasoning does not have to be all math related, but it should include specific values derived from calculations.
3. They ask the production team to make some candles for the sale. The team is not sure how many they can produce in the short time frame, so they ask for an acceptable range for how many of each candle they should make. Use the costs and recommended retail prices to make 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 the reasoning for these constraints. Graph the feasible region and find maximum and minimum profits.