The expected profit level of design K2 is $___, ( Enter your response as a real

Question

The expected profit level of design K2 is $___, (Enter your response as a real number rounded to two decimal places.)

The expected profit level of design K3 is $___, (Enter your response as a real number rounded to two decimal places.)

McBurger, Inc., wants to redesign its kitchens to improve productivity and quality. Three designs, called designs K1, K2, and K3, are under consideration. No matter which design is used, daily production of sandwiches at a typical McBurger restaurant is for 600 sandwiches. A sandwich costs $1.50 to produce. Non-defective sandwiches sell, on the average, for $2.50 per sandwich. Defective sandwiches cannot be sold and are scrapped. The goal is to choose a design that maximizes the expected profit at a typical restaurant over a 300-day period. Designs K1, K2, and K3 cost $115,000, $140,000, and 140,000, respectively. Under design K1, there is a .80 chance that 90 out of each 100 sandwiches are non-defective and a 20 chance that 70 out of each 100 sandwiches are non-defective. Under design K2, there is a.85 chance that 90 out of each 100 sandwiches are non-defective and a .15 chance that 75 out of each 100 sandwiches are non-defective. Under design K3, there is a .90 chance that 95 out of each 100 sandwiches are non-defective and a.10 chance that 80 out of each 100 sandwiches are non-defective. The expected profit level of design K1 is S (Enter your response as a real number rounded to two decimal places.)

Explanation / Answer

Under design K1, there is a .80 chance that 90 out of each 100 sandwiches are non-defective and a .20 chance that 70 out of each 100 sandwiches are non-defective.

Therefore, under design K1, Expected sale = (0.80 * 90 + 0.20 * 70) * (600/100) = 516 sandwiches

Under design K2, there is a .85 chance that 90 out of each 100 sandwiches are non-defective and a.15 chance that 75 out of each 100 sandwiches are non-defective.

Therefore, under design K2, Expected sale = (0.85 * 90 + 0.15 * 75) * (600/100) = 526.5 sandwiches

Under design K3, there is a .90 chance that 95 out of each 100 sandwiches are non-defective and a .10 chance that 80 out of each 100 sandwiches are non-defective.

Therefore, under design K3, Expected sale = (0.90 * 95 + 0.10 * 80) * (600/100) = 561 sandwiches

Now,

The expected profit level of design K1 = Revenue – Cost

= (Expected sale for design K1 per day * number of days in a year * Price/unit) – (Fixed cost of design K1 + variable cost per unit * number of units produced in a day * number of days in a year)

= (516 units* 300 * $2.50) – ($115,000 + $1.50 * 600 units *300)

= $387,000 – $385,000

= $2,000

The expected profit level of design K2 = Revenue – Cost

= (Expected sale for design K2 per day * number of days in a year * Price/unit) – (Fixed cost of design K2 + variable cost per unit * number of units produced in a day * number of days in a year)

= (526.5 units* 300 * $2.50) – ($140,000 + $1.50 * 600 units *300)

= $394,875 – $410,000

= - $15,125

The expected profit level of design K3 = Revenue – Cost

= (Expected sale for design K3 per day * number of days in a year * Price/unit) – (Fixed cost of design K3 + variable cost per unit * number of units produced in a day * Number of days in a year)

= (561 units* 300 * $2.50) – ($140,000 + $1.50 * 600 units *300)

= $420,750 – $410,000

= $10,750

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