Business Analytics B Answers

1. Determine the average profit that BA would earn if she orders 10,000 sweatshirts.

Solution:

Order 10,000Demand = 5,000 5,000*$30-10,000*$10 = $50,000

Demand = 10,000 10,000*$30-10,000*$10 = $200,000

Demand = 15,000 10,000*$30-10,000*$10 = $200,000

= 0.33 * $50,000 + 0.33 * $200,000 + 0.33 * 200,000

Answer: $148,500

2. How many sweatshirts would you recommend BA order to maximize expected profit?

Solution:

= 0.33 * $100,000 + 0.33 * $100,000 + 0.33 * 100,000= $99,000Demand = 5,000 5,000*$30-5,000*$10 = $100,000

Demand = 10,000 5,000*$30-5,000*$10 = $100,000

Demand = 15,000 5,000*$30-5,000*$10 = $100,000

Order 5,000

Order 10,000Demand = 5,000 5,000*$30-10,000*$10 = $50,000

= 0.33 * $50,000 + 0.33 * $200,000 + 0.33 * 200,000= $148,500Demand = 10,000 10,000*$30-10,000*$10 = $200,000

Demand = 15,000 10,000*$30-10,000*$10 = $200,000

Order 15,000Demand = 5,000 5,000*$30-15,000*$10 = $0

= 0.33 * 0 + 0.33 * $150,000 + 0.33 * 300,000= $148,500Demand = 10,000 10,000*$30-15,000*$10 = $150,000

Demand = 15,000 15,000*$30-15,000*$10 = $300,000

Answer: To maximize expected profit I recommend Beyond Armor to order either 10,000 or 15,000 sweatshirt.

3. Due to an outbreak of a novel infectious disease, Governor Hogan has announced that there is a 50% chance that all sport events will now be held without a live audience. If that happens, you will not be able to sell any sweatshirts for $30, and instead will only be able to sell to TJ Maxx and Marshalls, (in the same quantity as in the original problem formulation). How many sweatshirts would you recommend BA order to maximize average profit? Is the venture still profitable?

Solution:

RED FONT = NEGATIVE

= 0.33 * $10,000 + 0.33 * $10,000 + 0.33 * 10,000= $9,000Demand = 5,000 5,000*$12-5,000*$10 = $10,000

Demand = 10,000 5,000*$12-5,000*$10 = $10,000

Demand = 15,000 5,000*$12-5,000*$10 = $10,000

Order 5,000

Order 10,000Demand = 5,000 5,000*$12-10,000*$10 = ($40,000)

= 0.33 * ($40,000) + 0.33 * $20,000 + 0.33 * 20,000= $0Demand = 10,000 10,000*$12-10,000*$10 = $20,000

Demand = 15,000 10,000*$12-10,000*$10 = $20,000

Order 15,000Demand = 5,000 5,000*$12-15,000*$10 = ($90,000)

Demand = 10,000 10,000*$12-15,000*$10 = ($30,000)

= 0.33 * ($90,000) + 0.33 * ($30,000) + 0.33 * 30,000= ($29,700)Demand = 15,000 15,000*$12-15,000*$10 = $30,000

Answer: To maximize average profit I recommend Beyond Armor to order 5,000 sweatshirts. Yes it’s profitable by $9,000.