+8 I need help on the following questions: I have teacher hints
Info:
You work for the BeeSwaks Candle Company and have already updated the Brick and the Egyptian candles . The volume of the the brick is measured by the equation x^3-x^2. The volume of the Egyptian candle was marked by the equation 7x^2.
When comparing the graphs of the production volumes, after X> 8, the production of the Brick candle is greater proportion than the Egyptian candle. This result was to be expected, since the function of the Brick candle is a polynomial of degree 3, and the function of the Egyptian candle is a polynomial of degree 2. The volumes are equal at (8,448).
The same wax will be used to make each candle, and it costs 3 4 of 1¢ per cubic centimeter. Write polynomial functions to show the cost of the wax that is used for making each candle for different values of x. Graph the functions. Discuss the costs.
Question 1: You will redesigned the 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.
Hint:Look at your graphs and consider reasonable costs and volumes.
Question 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, 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.
Hint:Look at the graph of the cost functions. Find the costs for the dimensions that you chose. Remember that the goal is to make a profit after all costs are accounted for.
Question 3: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 create 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.
Hint:Writes a linear programming model that is accurate with their recommendations. ----> Think about the cost of each candle and what you set for the retail price. How much profit does each candle make? Make an objective function to find the total profit from selling a number of each candle. Also determine constraints for the number of candles requested from the factory. Keep in mind that it is a small sale and production time is limited. Think about the customers in the area where you will sell the candles. Do you think one of the models would sell better than the other?
Hint: Correctly graphs the feasible region. -----> Graph the lines based on your model. Because the factory manager asked for a range of each, you should have a closed feasible region.
Hint:Correctly finds the maximum profit. ------> Find the coordinates of the vertices of the feasible region. Find the pair that gives the greatest result.
Hint: Correctly finds the minimum profit. ------> Find the coordinates of the vertices of the feasible region. Find the pair that gives the smallest result.
