Question

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 500 sandwiches. A sandwich costs $1.40 to produce. Non-defective sandwiches sell, on the average, for $3.10 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 $120,000, $120,000, and $180,000, 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 $69900. (Enter your response as a real number rounded to two decimal places.) The expected profit level of design K2 is $ 78037.5. (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.)

Answer 1

For K1

Expected proportion of non-defective = 0.80 x (90/100) + 0.20 x (70/100) = 0.86

Volume production = 500 per day x 300 days = 150000

Profit = Selling price x Volume produced x Expected proportion of non-defective - Variable cost x Volume produced - Fixed cost
= 3.10 x 150000 x 0.86 - 1.40 x 150000 - 120000 = $69,900

For K2

Expected proportion of non-defective = 0.85 x (90/100) + 0.15 x (75/100) = 0.8775

Volume production = 500 per day x 300 days = 150000

Profit = 3.10 x 150000 x 0.8775 - 1.40 x 150000 - 120000 = $78,037.5

For K3

Expected proportion of non-defective = 0.90 x (95/100) + 0.10 x (80/100) = 0.935

Volume production = 500 per day x 300 days = 150000

Profit = 3.10 x 150000 x 0.935 - 1.40 x 150000 - 180000 = $44,775