Extra Credit Problems - Introduction

DSS 610 Business Analytics for MSBIA Student Name: Rawan Hawyan Extra Credit Problems (worth 10 points) 1. The Retread Tire Company recaps tires. The fixed annual cost of the recapping operation is $55,000.The variable cost of recapping a tire is $8.The company charges $21 to recap a tire. a. For an annual volume of 10,000 tires, determine the total cost, total revenue, and profit. Total Cost = Fixed annual cost + (Variable cost per unit × Annual volume) = $55000 + ($8 × 10,000) = $135,000 Total Revenue = sales price per unit × volume = $21 × 10000 = $210,000 Profit = Total Revenue – Total Cost = $210.000 – 135,000 = $75,000 b. Determine the annual break-even volume for the Retread Tire Company operation. Break-even volume = ¿ Costs Sales price per unit − Variable cost per unit Break-even volume = 55,000 21 − 8 ≈ 4,231 Units 2. Evergreen Fertilizer Company produces fertilizer. The company’s fixed monthly cost is $30,000, and its variable cost per pound of fertilizer is $0.16. Evergreen sells the fertilizer for $0.40 per pound. Determine the monthly break-even volume for the company. Break-even volume = ¿ monthly costs Selling price per pound − Variable cost per pound Break-even volume = 30,000 0.40 − 0.16 = 125,000 pounds per month.

DSS 610 Business Analytics for MSBIA 3. If Evergreen Fertilizer Company in Problem 2 changes the price of its fertilizer from $0.40 per pound to $0.60 per pound, what effect will the change have on the break-even volume? Break-even volume = ¿ monthly costs Selling price per pound − Variable cost per pound Break-even volume = 30,000 0.60 − 0.16 ≈ 68,181 pounds per month. The effect will be as follows: break-even volume will decrease from 125,000 to 68,181 pounds per month when we change the price of its fertilizer from $0.40 per pound to $0.60 per pound. 4. If Evergreen Fertilizer Company increases its advertising expenditures by $14,000 per year, what effect will the increase have on the break-even volume computed in Problem 2? Fixed Cost = $30,000 + $14,000 = $44,000 Variable cost per unit = $0.16 Selling price of unit = $0.40 Break-even volume = ¿ monthly costs Selling price per pound − Variable cost per pound Break-even volume = 44,000 0.40 − 0.16 ≈ 183,333 pounds per month. The effect is Break-even volume is increased due to an increment in the fixed cost. 5. Annie McCoy, a student at Tech, plans to open a hot dog stand inside Tech’s football stadium during home games. There are seven home games scheduled for the upcoming season. She must pay the Tech athletic department a vendor’s fee of $2,500 for the season. Her stand and other equipment will cost her $3,100 for the season. She estimates that each hot dog she sells will cost her $0.35. She has talked to friends at other universities who sell hot dogs at games. Based on their information and the athletic department’s forecast that each game will sell out, she anticipates that she will sell approximately 2,000 hot dogs during each game.

DSS 610 Business Analytics for MSBIA b. If the college can enroll 75 students the first year, how much profit will it make? Fixed cost = $360000 Selling Price = $17,000 per student per year Variable cost = $12,000 per student per year Total Annual Revenue = Selling price per student per year x 75 = $17,000 x 75 = $1,275,000 Total Annual Variable cost = Variable cost per student per year x 75 = 12000 x 75 = $ 900,000 Profit = Total Annual Revenue - Fixed cost - Total Annual Variable cost = 1,275,000 – 360,000 - 900,000 = $375,000 So, first year profit by 75 students = $15,000 c. The college believes it can increase tuition to $22,000, but doing so would reduce enrollment to 35. Should the college consider doing this? Total Annual Revenue = 22,000 × 35 = $770,000 Total Annual Variable cost = 12,000 × 35 = $420,000 Profit = $770,000 – $360,000 - $420,000 = $ -10,000 So, this decision will be irrational, and the college shouldn't do that. 7. The following probabilities for grades in management science have been determined based on past records: Grade Probability A 0.15 B 0.25

DSS 610 Business Analytics for MSBIA C 0.38 D 0.12 F 0.10 1.00 The grades are assigned on a 4.0 scale, where an A is a 4.0, a B a 3.0, and so on. Determine the expected grade and variance for the course. Grade x P(x) x * P(x) x 2 * P(x) A 4 0.15 0.6 2.4 B 3 0.25 0.75 2.25 C 2 0.38 0.76 3 D 1 0.12 0.12 0.12 F 0 0.10 0 0 Total 1.00 2.23 7.77 Expected Grade E(x) = ∑ x ¿ P(x) = 2.23 Variance V(x) = ∑ x 2 ∗ P ( x ) − E ( x ) 2 = 7.77 − 4.9729 ≈ 2.8 8. The weight of bags of fertilizer is normally distributed, with a mean of 50 pounds and a standard deviation of 7 pounds. What is the probability that a bag of fertilizer will weigh between 45 and 55 pounds? Population means: μ = 50 pounds Population standard deviation: σ = 7 pounds P(45 ¿ X < 55 ¿ = P ( 45 − 55 7 < x − μ σ < 55 − 50 7 ) = P( -0.7143 ¿ Z ¿ 0.7143) = P(z ¿ 0.7143) – P(z ¿ -0.7143) = 0.76248 – 0.23752 = 0.5250 The probability that a bag of fertilizer will weigh between 45 and 55 pounds = 0.5250

DSS 610 Business Analytics for MSBIA k − μ σ = 1.28 k = 256.8 Number of recorders the manager should order each month to meet 90% of customer demand ≈ 257 Recorders.