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

$1.30

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

$100,000​,

$130,000​,

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

​$nothing.

​(Enter

your response as a real number rounded to two decimal

places.​)

The expected profit level of design K2 is

​$nothing.

​(Enter

your response as a real number rounded to two decimal

places.​)

The expected profit level of design K3 is

​$nothing.

​(Enter

your response as a real number rounded to two decimal

places.​)

What is the expected profit level of the design that achieves the maximum expected​ 300-day profit​ level?

Design

▼

K1

K2

K3

achieves the maximum expected​ 300-day profit​ level, with a profit of

​$nothing.

​(Enter

your response as a real number rounded to two decimal

places.​)

Answer 1

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 = 150,000
Profit = Selling price x Volume produced x Expected proportion of non-defective - Variable cost x Volume produced - Fixed Cost = $2.50 x 150,000 x 0.86 - $1.30 x 150,000 - 120,000 = $247,500

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 = 150,000
Profit = $2.50 x 150,000 x 0.8775 - $1.30 x 150,000 - 120,000 = $254,062.50

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 = 150,000
Profit = $2.50 x 150,000 x 0.935 - $1.30 x 150,000 - 180,000 = $335,625

So, by the above calculations the expected profit level of the design that achieves the maximum expected 300-day profit level is The Design K3 with $335,625 of expected profit level.

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