Johnson Electronics sells electrical and electronic components through catalogs. Catalogs are printed once every two years. Each printing run incurs a fixed cost of $25,000, with a variable production cost of $5 per catalog. Annual demand for catalogs is estimated to be normally distributed with a mean of 16,000 and standard deviation of 4,000. Data indicate that, on average, each customer ordering a catalog generates a profit of $35 from sales. Assuming that Johnson wants only one printing run in each two-year cycle, how many catalogs should be printed in each run

Respuesta :

Answer:

$38,029

Explanation:

Sales of p = $35

Costs w = $5.00 (Production)

Assumption →v = 0 B = p‑w = 35‑5 = 30

C = w‑v = 5

Prob(D £ Q*) = SL*= B/(B+C) = 30/(30+5) = 0.8571

The z‑value matching to 0.8571 is 1.068 using the normal distribution table

Therefore the total demand for 2 years (D): Mean of m = 2 ×16,000 = 32,000

Standard Deviation (square root(2)X 4000= 5,657

Optimal Order Quantity (Q*)= m + zs =

$32,000 + 1.068×5,657 = $38,039