The Retread Tire Company Recaps Tires The Fixed Ann

The Retread Tire Company Recaps Tires The Fixed Ann

Week 1 Homework 1. The Retread Tire Company recaps tires. The fixed annual cost of the recapping operation is $65,000. The variable cost of recapping a tire is $7.5. The company charges $25 to recap a tire. a. For an annual volume of 15,000 tires, determine the total cost, total revenue, and profit. b. Determine the annual break-even volume for the Retread Tire Company operation. MAT540 Homework Week 1 2. Evergreen Fertilizer Company produces fertilizer. The company’s fixed monthly cost is $25,000, and its variable cost per pound of fertilizer is $0.20. Evergreen sells the fertilizer for $0.45 per pound. Determine the monthly break-even volume for the company. 3. If Evergreen Fertilizer Company in problem 2 changes the price of its fertilizer from $0.45 per pound to $0.55 per pound, what effect will the change have on the break-even volume? 4. If Evergreen Fertilizer Company increases its advertising expenditure by $10,000 per year, what effect will the increase have on the break-even volume computed in problem 2? 5. Annie McCoy, a student at Tech, plans to open a hot dog stand inside Tech’s football stadium during home games. There are 6 home games scheduled for the upcoming season. She must pay the Tech athletic department a vendor’s fee of $3,000 for the season. Her stand and other equipment will cost her $3,500 for the season. She estimates that each hot dog she sells will cost her $0.40. She anticipates selling approximately 1,500 hot dogs during each game, based on forecasts that each game will sell out. a. What price should she charge for a hot dog to break even? b. What factors might alter the volume sold and the break-even price? 6. The college of business at Kerouac University plans to start an online MBA program. The startup costs are $400,000. The college plans to charge $20,000 per student annually, but the university will charge $10,000 per student for administrative costs for the first 100 students. a. How many students are needed to break even? b. If enrollment is 80 students, what is the profit? c. Should the college increase tuition to $25,000 with expected enrollments of 50 students? 7. Probabilities for grades in management science are: A 0.1, B 0.2, C 0.4, D 0.2, F 0.0. Grades are on a 4.0 scale: A=4.0, B=3.0, etc. Determine the expected grade and variance. 8. An investment firm considers two investments, A and B, under good and poor economic conditions with respective probabilities 0.60 and 0.40. Expected gains/losses are given for each. Use expected value to decide which investment to select. 9. The weight of fertilizer bags is normally distributed with mean 45 pounds and SD 5 pounds. Find the probability that a bag weighs between 38 and 50 pounds. 10. A shopping center is estimated to be completed in 15 months with SD 5 months. Construction is actually expected to take 18 months. What is the probability that tenants cannot occupy by then? 11. A video store manager wants to stock inventory to meet 85% demand to minimize costs. Monthly demand for recorders is normally distributed with mean 175 and SD 55. Determine the order quantity to meet 85% of demand.

Paper For Above instruction

This comprehensive analysis addresses several managerial problems involving cost-volume-profit analysis, break-even points, expected value calculations, probability assessments, and inventory management within various business contexts. The goal is to demonstrate the application of quantitative methods to decision-making scenarios typical in operations and managerial finance, illustrating fundamental concepts and calculations critical for business managers and students alike.

Initially, the problem involving the Retread Tire Company focuses on understanding the core components of cost behavior and profit analysis. With a fixed annual cost of $65,000 and a variable recapping cost of $7.5 per tire, coupled with a selling price of $25, the firm’s total cost, total revenue, and profit at a specified volume illuminate the impact of sales volume on profitability. The total cost is calculated by summing fixed costs and variable costs (which depend on volume), while total revenue derives from multiplying volume by unit price. Profit emerges as the difference between total revenue and total costs. For an annual volume of 15,000 tires:

• Total Variable Cost (TVC): 15,000 × $7.5 = $112,500
• Total Cost (TC): Fixed Cost + TVC = $65,000 + $112,500 = $177,500
• Total Revenue (TR): 15,000 × $25 = $375,000
• Profit: TR – TC = $375,000 – $177,500 = $197,500

The break-even analysis requires finding the volume where total revenue equals total cost:

• Let x be the break-even volume, then:

  TR = TC

  $25x = $65,000 + $7.5x

  $25x – $7.5x = $65,000

  $17.5x = $65,000

  x = $65,000 / $17.5 ≈ 3,714 tires

This indicates the company would need to sell approximately 3,714 tires annually to break even.

Next, the Evergreen Fertilizer Company’s scenario demonstrates the fundamentals of break-even analysis with a fixed cost of $25,000 per month and a variable cost of $0.20 per pound, sold at $0.45 per pound. The monthly break-even volume is computed by dividing fixed costs by the contribution margin per unit:

• Contribution margin per pound: $0.45 – $0.20 = $0.25
• Break-even volume: $25,000 / $0.25 = 100,000 pounds

If the price increases to $0.55 per pound, the contribution margin becomes $0.35, reducing the break-even volume:

• New break-even volume: $25,000 / $0.35 ≈ 71,429 pounds

An increase in advertising expenditure by $10,000 per year impacts the fixed costs:

• New fixed monthly cost: $25,000 + ($10,000 / 12) ≈ $25,833
• New break-even volume: $25,833 / $0.25 ≈ 103,333 pounds

The hot dog stand case involves calculating the selling price needed to break even, considering fixed costs and variable costs per hot dog, with assumptions about volume based on sell-out forecasts. The break-even price is set where total revenue equals total costs:

• Total fixed costs: $3,000 (vendor fee) + $3,500 (equipment) = $6,500
• Variable cost per hot dog: $0.40
• Sales volume: 1,500 hot dogs per game × 6 games = 9,000 hot dogs
• Total variable costs: 9,000 × $0.40 = $3,600

Total costs: $6,500 + $3,600 = $10,100

Therefore, the break-even price per hot dog:

• Break-even price: $10,100 / 9,000 ≈ $1.12

Factors affecting volume and pricing include weather conditions, competing vendors, and changes in demand that could alter forecasted sales, thus influencing the revenue needed to break even.

Concerning the online MBA program at Kerouac University, the initial startup costs total $400,000, with fixed tuition revenues of $20,000 per student and an administrative fee of $10,000 per student for the first 100 students. To find the breakeven point:

• Revenue per student: $20,000
• Per-student cost to the college: $10,000
• Net contribution per student: $10,000
• Number of students needed to recover start-up costs:

  $400,000 / $10,000 = 40 students

If enrollment is 80 students, the profit would be:

• Total contribution: 80 × $10,000 = $800,000
• Profit: $800,000 – $400,000 = $400,000

Increasing tuition to $25,000 per student, with only 50 enrollments, yields:

• Total revenue: 50 × $25,000 = $1,250,000
• Costs: $400,000 (startup only, assuming fixed costs are sunk), profit: $1,250,000 – $400,000 = $850,000

This indicates higher profit potential, suggesting the college should consider the price increase if market conditions allow.

The grades probability problem involves calculating the expected value and variance of grades based on given probabilities:

• Expected grade (E): E = Σ (grade value × probability)

  = (4.0 × 0.1) + (3.0 × 0.2) + (2.0 × 0.4) + (1.0 × 0.2) + (0 × 0)

  = 0.4 + 0.6 + 0.8 + 0.2 + 0 = 2.0

• Variance involves calculating the expected value of the squared grades minus the square of the expected value:

  σ² = E[X²] – (E[X])²

  First, compute E[X²]:

  E[X²] = (4.0² × 0.1) + (3.0² × 0.2) + (2.0² × 0.4) + (1.0² × 0.2) + (0² × 0)

  = (16 × 0.1) + (9 × 0.2) + (4 × 0.4) + (1 × 0.2)

  = 1.6 + 1.8 + 1.6 + 0.2 = 5.2

  Thus, variance:

  σ² = 5.2 – (2.0)² = 5.2 – 4 = 1.2

Investment options are evaluated based on expected gains and economic condition probabilities:

• Expected value of Investment A:

  EV_A = (0.60)(\$380,000) + (0.40)(–\$100,000) = \$228,000 – \$40,000 = \$188,000

• Expected value of Investment B:

  EV_B = (0.60)(\$130,000) + (0.40)(\$85,000) = \$78,000 + \$34,000 = \$112,000

Choosing the investment with the higher expected value, Investment A is preferable.

The propane bag weight query relies on calculating the probability within a normal distribution:

• Z-scores:

  Z1 = (38 – 45) / 5 = –1.4

  Z2 = (50 – 45) / 5 = 1.0

  Using standard normal distribution tables, the probabilities:

  P(Z

  P(Z

  The probability that weight is between 38 and 50 pounds:

  P = P(Z

Finally, the construction project’s probability of delay involves the normal distribution:

• Calculating the probability that the actual completion time exceeds 18 months:

  Z = (18 – 15) / 5 = 0.6

  From standard normal tables:

  P(Z > 0.6) ≈ 1 – 0.7257 = 0.2743

  Indicating about a 27.43% chance.

Inventory management for the video store involves determining the order quantity for 85% service level:

• Using the z-score for 85% confidence level: z ≈ 1.04
• Order quantity:

  Q = mean demand + z × SD = 175 + 1.04 × 55 ≈ 175 + 57.2 ≈ 232 recorders

This ensures meeting 85% of demand while balancing inventory costs.

In conclusion, these varied scenarios exemplify key quantitative decision tools in operations management, finance, and marketing. Employing cost analysis, break-even calculations, probability assessments, and expected value computations allows managers to make informed, data-driven decisions across diverse business contexts. Knowledge of these techniques enhances strategic planning, risk assessment, and operational efficiency in the increasingly complex landscape of modern business environments.

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