Associate Level Material
Appendix C
Polynomials
Retail companies must keep close track of their operations to maintain profitability. Often, the sales data of each individual product is analyzed separately, which can be used to help set pricing and other sales strategies.
Application Practice
Answer the following questions. Use Equation Editor to write mathematical expressions and equations. First, save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting.
In this problem, we analyze the profit found for sales of decorative tiles. A demand equation (sometimes called a demand curve) shows how much money people would pay for a product
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Let x represent the number of tile sets. If b represents a fixed cost, what value would represent b?
Find the cost equation for the tile. Write your answer in the form C = mx + b.
The profit made from the sale of tiles is found by subtracting the costs from the revenue.
Find the Profit Equation by substituting your equations for R and C in the equation . Simplify the equation. What is the profit made from selling 20 tile sets per month?
What is the profit made from selling 25 tile sets each month?
What is the profit made from selling no tile sets each month? Interpret your answer.
Use trial and error to find the quantity of tile sets per month that yields the highest profit.
How much profit would you earn from the number you found in part i?
What price would you sell the tile sets at to realize this profit? Hint: Use the demand equation from part a.
The break even values for a profit model are the values for which you earn $0 in profit. Use the equation you created in question one to solve P = 0, and find your break even values.
In 2002, Home Depot’s sales amounted to $58,200,000,000. In 2006, its sales were $90,800,000,000.
Write Home Depot’s 2002 sales and 2006 sales in scientific notation.
You can find the percent of growth in Home Depot’s sales from 2002 to 2006 by following these steps:
Find the increase in sales from 2002 to 2006. Find what percent that
Assume that next year management wants the company to earn a minimum profit of $162,000. How many units be sold to meet this target profit figure? [3 points]
In our second assumption, instead of using the cost of goods per cases in 1986, we try to use the percentage it counts in the total expenses which is 50.4% and to find the sales needed to break-even. The detail of the calculation is shown in the answer for questions d. The result is that 95,635, a little bit higher than the estimated sales of 90,000.
Actual sales = 1686 (in million €) and Break even sales = 1126.61(in million €)
1. The local Mastermind store sells innovative educational toys. Part of their service is giving advice to customers about the best toys for a particular age group, which requires having more customer service representatives in the store. During the month long Christmas buying season, it makes half of its $500,000 yearly sales. Its contribution margin on average is 40% and its fixed costs for the year are about $150,000. The owner believes that she could make even higher sales, if she had more customer service representatives on the floor during the peak season. She plans on hiring four more people for 200 hours each at $20 per hour. How much additional revenue does she have earn to the nearest dollar
The new owner of a beauty shop is trying to decide whether to hire one, two, or three beauticians. She estimates that profits next year (in thousands of dollars) will vary with demand for her services and has estimated demand in three categories low, medium and high.
* Use the profit maximization rule MR = MC to determine your optimal price and optimal output level now that you have market power. Compare these values with the values you generated in Assignment 1. Determine whether your price higher is or lower.)
For example, for the month of October, 23 days (6 days per week times 4 weeks) at 1,000 expected units plus Halloween's expected unit sales (1,500) equaled 24,500 units times the price of$3.50 equaled the total net sales for the month of October of $85,750. The same formula was used for the months of November and December in an attempt to budget from one month to the next. The total 4th quarter sales budget, with the holiday expected unit sales came to a total of $250,950. These totals can be used as the comparison budget for next year's budgeting since this is the first year for Babycakes in LA. The figures presented are strictly sales predictions and do not include daily operations cost.
Profit: $686,670 ($225*$5,000= $1,125,000 (Revenue); $75*4,000=$300,000 + $50,000/4,000= $87.50 (Unit Cost); $87.50*4,000= $350,000 + $83,330= $433,330
The starting daily budget is $40.00, due to $1200.00 being the amount of money we can afford to lose. The predicted cost per click is $3.00 and the aver profit per conversion is $20.00. The conversion rate at 15% allows us to break even.
a. For an annual volume of 12,000 tires, determine the total cost, total revenue, and profit.
A result on the next page shows that at sales price of $21.50, the sales quantity rises to 1,140,085 units and net profit turns to positive for the first time. Besides, if a company continues to reduce the price further, at the point of $15.50, it is where the company’s profit on product 101 is in the highest position as it gives the net profit of $3,901,908.
23. Utilzing the formula dictated in question 23, = 0.12*B6^2+0.02*C6^3+3.5*SQRT(D6)+0.05*E6*F6 this calcualated an answer for Ann's profit at $862.03.
Question B: How many units per year must be sold with each process to have annual profits of $50,000 if the selling price is $6.95 per unit?
- The Total profit can be computed by adding benefits extracted form each material : (4.4S1+4.4R1+1.95P1+4.2S2+4.2R2+2.15P2+4.7S3+4.7R3+ 2.35P3+5.5S4+2.6P4+5.7S5+2.75P5+6.05S6+2.9P6)