Question

Suppose a grocery store buys milk (in gallon jugs) using the EOQ model with quantity discounts.

Holding cost is $0.10 per gallon per day

Order placement cost is $20, regardless of size

Weekly demand is 350 gallons

The milk supplier offers two discount levels for order quantity Q:

$0.05 per gallon when 100 gal. ? Q < 200 gal.

$0.045 per gallon when Q ? 200 gal.

What order quantities need to be checked?

What is the economic order quantity?

Answer 1

1. One gallon of milk weighs 8.6 lbs, how many gallons of milk would it take to equal your weight?

2. If a cow produces about 70 pounds of milk per day, how many gallons is that (round your answer to the nearest whole number)?

3. There are 8 pints in a gallon. If one milk carton is ½ pint, how many milk cartons of milk does a cow produce each day (hint: use the answer from Question #2).

4. If each student in your class drank one carton of milk at breakfast and one carton at lunch, how many gallons would that be? How many cows will it take to make that much milk?

5. If you can milk 80 cows each hour, how long will it take to milk 640 cows?

6. On your farm, cows can be milked in groups of five cows at a time. If you have 13 cows left, and will only bring in 3 groups, what are the ways that the cows can be grouped?

7. On your neighbor’s farm, the cows are 58 inches tall and 23 inches wide. She asks you to help her plan her new barn. To make sure the cows are comfortable in their stalls, you multiply their height by two to find the length of the stall and their width by two to find the width of the stall.  Using these formulas, what should the dimensions of the stall be?

8. In Wisconsin, 89.1% of farms are owned by individuals and families, 6.9% are owned by partnerships of families, 3.3% are owned by family corporations, and 0.7% are ‘other’. What percentage of Wisconsin farms are owned by some sort of family? Draw a pie chart of the Wisconsin Dairy Farm Ownership using this data.

ANSWER KEY

1. One gallon of milk weighs 8.6 lbs, how many gallons of milk would it take to equal your weight?

Answers will vary depending on the weight of the student!

95 lbs (use the student’s weight) /8.6 lbs of milk in one gallon =

11.04 gallons of milk to equal student weight

2. If a cow produces about 70 pounds of milk per day, how many gallons is that (round your answer to the nearest whole number)?

70 lbs / 8.6 lbs per gallon =8.1 or rounded to 8

3. There are 8 pints to a gallon. If one milk carton is ½ pint, how many milk cartons of milk does a cow produce each day (hint: use the answer from Question #2).

2 cartons in a pint X 8 pints in a gallon = 16 cartons in a gallon

8 gallons produced each day X 16 cartons per gallon = 128 cartons of milk

produced in one day

4. If each student in your class drank one carton of milk at breakfast and one carton at lunch, how many gallons would that be? How many cows will it take to make that much milk?

Answers will vary depending on the number of students in the class!

24 students in the class X 2 cartons each day = 48 cartons

48 cartons / 16 cartons in a gallon =3 gallons

8 gallons per cow per day / 3 gallons needed by the class = 2.6 (one cow could produce two and a half days worth of milk for the class)

5. If you can milk 80 cows each hour, how long will it take to milk 640 cows?

640 cows / 80 cows per hour = 8 hours to milk 640 cows

6. On your farm, cows can be milked in groups of five cows at a time. If you have 13 cows left, and will only bring in 3 groups, what are the ways that the cows can be grouped?

Group One: five cows, Group Two: five cows, Group Three: three cows

Group One: five cows, Group Two: four cows, Group Three: four cows

7. On your neighbor’s farm, the cows are 58 inches tall and 23 inches wide. She asks you to help her plan her new barn. To make sure the cows are comfortable in their stalls, you multiply their height by two to find the length of the stall and their width by two to find the width of the stall. Using these formulas, what should the dimensions of the stall be?

58 inches long X 2 =116 inches for the stall length

23 inches wide X 2 = 46 inches for the stall width

8. In Wisconsin, 89.1% of farms are owned by individuals and families, 6.9% are owned by partnerships of families, 3.3% are owned by family corporations, and 0.7% are ‘other’. What percentage of Wisconsin farms are owned by some sort of family?

89.1 + 6.9 + 3.3 = 99.3%

Draw a pie chart of the Wisconsin Dairy Farm Ownership using this data.