Question

Nancy has started a new career in newspaper delivery. She has established a small stand in her front yard (with proper municipal forms filed, of course) from which she sells the well-known national weekly newspaper, GRIT, each week. She purchases GRIT from the company for $1.00 per copy, and sells it for $2.00 per copy. Any unsold copies can be sent back to the company for $0.50 credit per copy. Over a long period of time, a fairly consistent pattern of sales has emerged, according to the following probability distribution. (Remember that GRIT is a weekly newspaper.) Sales P(Sales) 20 0.10 30 0.25 40 0.40 0.25 Under the assumption that Nancy would only obtain stock to match one of the demand levels above, how many GRIT should she stock (purchase) each week in order to maximize profit over the long run?

Answer 1

As given,

Cost price per unit = $2

Selling price per unit = $1

Unsold return per unit = $0.5

Profit if all stock are sold (per unit) = $2- $1= $1

Loss if unsold stock is returned back = $0.5- $1 = - $0.5

Now, we will create a table to compare each option of stocking as per demand level (in rows) and actual sales (in column) to find out the net profit/ loss in combination of scenarios. We will then find the expected value using probability of sales given.

	Sales=20	Sales=30	Sales=40	Sales =50
Probability - P(Sales)	0.1	0.25	0.4	0.25	Expected Profit
Stock = 20	$1*20=$20	$1*20=$20	$1*20=$20	$1*20=$20	$20*0.1+$20*0.25+$20*0.4+$20*0.25 = $20
Stock = 30	1*20+(30-20)*(-0.5)= $15	1*30= $30	1*30= $30	1*30= $30	15*0.1+30*0.25+30*0.4+30*0.25=$28.5
Stock = 40	$1*20+(40-20)*(-0.5)=$10	$1*30+(40-30)*(-0.5)=$25	1*40= $40	1*40= $40	10*0.1+25*0.25+40*0.4+40*0.25= $33.25
Stock = 50	$1*20+(50-20)*(-0.5)=$5	$1*30+(50-30)*(-0.5)=$20	$1*40+(50-40)*(-0.5)=$35	1*50= $50	5*0.1+20*0.25+35*0.4+50*0.25= $32.00

Highest expected profit is for stock = 40 ($33.25).

Hence, GRIT should stock 40 each week in order to maximize profits.

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