THE DRY-CLEANING PROBLEM

THE DRY-CLEANING PROBLEM

Mr. Brown has a dry cleaning shop.  They only make dry cleaning for items on table in below. According to Mr. Brown, the price of spent cleaning materials is 1 Lira for each item, and the expenditures for electricity are 19.0 kw/h for cleaning machine and 12.0 kw/h for the iron which they use. Mr. Brown and his workers can do maximum 128 hours for cleaning and 110 hours for ironing in a week because of the heating problems of machines. So, they clean them in the other week or they reject them if there are extra items. They can clean at most 40 suits within a week because their cleaning is taking more time the others. There is given information that the cost of 1 kw/h electricity is equal to 0.40 Lira. Also, they make ironing if they make cleaning.

According to given information answer the questions below:

PART I) 2 hours for cleaning and 1 hour for ironing is required to complete the dry cleaning of the suit (jackets + pants). 1 hour for cleaning and 1 hour for ironing is required to complete the dry cleaning of the night dress.

  1. Which product must be cleaned for more profit by considering given situations ? Suit or night dress?
  2. How many suit and night dress should be cleaned in the week that they have the most profit if they clean only suits and night dresses?
  3. What is the difference between the results of ‘’part a’’ and ‘’part b’’? Why?
  4. How part b will change if there is no restriction for cleaning and ironing hours?

PART II) Mr. Brown decides to make campaign to increase customers and he says; there will be 10% discount for every customer who bring 5 pieces of same item and above, and there will be 25% discount for every customer who bring 10 pieces of same item and above. A customer wishes to benefit from the campaign. Which product can be brought to make customers more profitable?

(Hint: do not consider the restrictions such as ironing and cleaning hours.)

 

 

Items

Cleaning

Ironing

Shirt

9,90 Liras

4,95 Liras

Skirt

12,90 Liras

6,45 Liras

Jacket

16,90 Liras

8,45 Liras

Pleated skirt

16,90 Liras

8,45 Liras

Topcoat

22,90 Liras

11,45 Liras

Coat

22,90 Liras

11,45 Liras

Tie

6,90 Liras

3,45 Liras

Pants

12,90 Liras

6,45 Liras

Pullover

12,90 Liras

6,45 Liras

Mont

16,90 Liras

8,45 Liras

Blouse

16,90 Liras

8,45 Liras

Night dress

22,90 Liras

11,45 Liras

Scarf

6,90 Liras

3,45 Liras

 

01 Haziran 2018 Cuma
RABİYA YİĞİT
MATEMATİK - KONYA