Question

Johnson Electronics sells electrical and electronic components through catalogs. Catalogs are updated and printed twice every year. Each printing run incurs a fixed cost of $5,000, which involves catalog design cost and printing setup cost. The variable production cost is $5 per catalog. The half-year demand for catalogs is estimated to be normally distributed with a mean of 8,000 and standard deviation of 3,000. Data indicate that, on average, each customer ordering a catalog generates a profit of $35 from sales. How many catalogs should be printed?

Answer 1

Answer:

optimal order quantity is 11450

Explanation:

solution

we will use here news vendor model here

and profit means that if we print less we will incur a certain opportunity loss

so it is known as cost of understocking (Cu) i.e = 35

and

production cost = $5

when product is not sold

we incur  cost of (Co) i.e = 5

so

fixed cost is incurred either way in a year

so we need to consider the critical fractile value

that is express as

CF = $\frac{Cu}{Cu + Co}$

CF = $\frac{35}{35 + 5}$

CF = $\frac{35}{40}$

CF = 0.875

so value of Z at  0.875   is 1.15

so

means the optimal order per production will be here =  8000 + 1.15 ×3000 = 11450

so

optimal order quantity is 11450