The demand for next year\'s calendar at a bookstore is assumed to be normally di

Question

The demand for next year's calendar at a bookstore is assumed to be normally distributed with a mean of 430 and a standard deviation of 70. The calendar costs the bookstore $7.00 each and will be sold for $11.00 each. Any calendars remaining for sale after the new year will be discounted and sold for $1.30 each. The bookstore believes ALL the remaining calenders to be sold after the new year will be sold at the $1.30 price. How many calendars should the bookstore stock if it wants to maximize its expected profit from calendars?

Explanation / Answer

Purchase cost = $7.00 per calendar

Selling price = $11.00 per calendar

Salvage value = $1.50 per calendar

Mean demand = µ = 230 calendars

Standard Deviation = = 70 calendars

For the given data apply single-period Inventory model

Cs = cost of shortage (underestimate demand) = Sales price/unit – Cost/unit

Co = Cost of overage (overestimate demand) = Cost/unit – Salvage value /unit

Cs = 11 – 7 = $4 per pound

Co = 7 – 1.5 = $5.5 per pound

The service level or probability of not stocking out, is set at,

Service Level = Cs/( Cs + Co) = 4/(4 + 5.5) = 4/9.5

Service Level = 0.4210

Bookstore assistant needs to find the Z socre for the demand normal distribution that yields a probability of 0.421.

So 42.10% of the area under the normal curve must be to the right of the optimal stocking level.

Using standard normal table, for an area of 0.4167, the Z score is -0.1993.

Optimal order quantity = µ + z = 430 + (-0.1993)70

Optimal order quantity = 416 calendars

Bookstore should order 416 calendars to maximize expected profit.

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