Question

Wholemark is an Internet order business that sells one popular New Year greeting card once a year. The cost of the paper on which the card is printed is $0.40 per card, and the cost of printing is $0.10 per card. The company receives $3.75 per card sold. Since the cards have the current year printed on them, unsold cards have no salvage value. Their customers are from the four areas: Los Angeles, Santa Monica, Hollywood, and Pasadena. Based on past data, the number of customers from each of the four regions is normally distributed with mean 2,300 and standard deviation 200. (Assume these four are independent.)
What is the optimal production quantity for the card?

Answer 1

Answer:

≈ 9644 quantity of card

Explanation:

given data:

n = 4 regions/areas

mean demand = 2300

standard deviation = 200

cost of card (c) = $0.5

selling price (p) = $3.75

salvage value of card ( v ) = $ 0

The optimal production quantity for the card can be calculated using this formula below

= u + z (0.8667  ) * б

= 9200  +  1.110926 * 400

≈ 9644 quantity of card

First we have to find u

u = n * mean demand

 = 4 * 2300 = 9200

next we find the value of Z

Z = ( $\frac{p-c}{p-v}$ )

   = ( 3.75 - 0.5 ) / 3.75   = 0.8667

Z( 0.8667 ) = 1.110926 ( using  excel formula : NORMSINV (0.8667 )

next we find б

б = 200$\sqrt{n}$ = 400