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Daily demand for fresh cauliflower in the ZZ-Warehouse store follows normal distribution with mean 100 cartons and s.d. 20 cartons. The ZZ-Warehouse buys at a cost of $50.00 per carton, sells it for $70.00 per carton. Unsold cartons are sold for $20.00 per carton. What is the optimal order quantity, using the single period model?

Respuesta :

Answer: The optimal order quantity would be 95 approximately.

Explanation:

Since we have given that

Mean = 100 cartons

SD= 20 cartons

Cost price per carton = $50.00

Selling price per carton = $70.00

Salvage cost = $20.00

Underage cost = Selling  price - cost price

[tex]C_u[/tex] = [tex]70-50=20[/tex]

Overall cost = Cost price - Salvage

[tex]C_o=50-20=30[/tex]

So optimality proportion would be

[tex]\dfrac{C_u}{C_o+C_u}\\\\=\dfrac{20}{20+30}\\\\=\dfrac{20}{50}\\\\=0.4[/tex]

At p = 0.4, so z = -0.253

So, it becomes,

[tex]q=\mu+z\times \sigma\\\\q=100-0.253\times 20\\\\q=100-5.06\\\\q=94.94[/tex]

So, the optimal order quantity would be 95 approximately.

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