Question

Suppose the owner of a local apple orchard has 4 half-bushels of apples to sell. He loads them on his truck, and drives his route, stopping at stores along the way attempting to sells the apples. Suppose:
- Each half-bushel is sold for $40.

- It will cost $15 of gas to drive the route.

Historically, the orchard owner knows he will have a 40% chance of making no sales, a 30% chance of selling 1 half-bushel, a 10% chance of selling 2 half-bushels, and a 10% chance of selling 3 half-bushels.

(a) Calculate the orchard owner’s expected profit from driving the route.

(b) Calculate the standard deviation of the profit from driving the route.

Answer 1

Answer:

a) The orchard owner's expected profit from driving the route is $33.

b) The standard deviation of the profit is $27.28

Step-by-step explanation:

a) Data and Calculations:

Apples to sell = 4 half-bushels

Price of each half-bushel sold = $40

Sales revenue = $160 ($40 *4)

Cost of driving the route = $15

Expected values:

Event                          Probability  Revenue       Profit         Expected  Profit

No Sales                        40%            $0         ($15) ($0 - $15)        ($6.00)

Selling 1 half-bushel      30%         $40         $25 ($40 - $15)         $7.50

Selling 2 half-bushels   10%          $80         $65 ($80 - $15)        $6.50

Selling 3 half-bushels   10%         $120       $105 ($120 - $15)     $10.50

Selling 4 half-bushels   10%         $160       $145 ($160 - $15)     $14.50

Total expected profit = $33

Event                          Expected  Profit  Mean        Squared

                                                                       Difference

No Sales                            ($6.00)        -39             1,521

Selling 1 half-bushel           $7.50         -25.5           650.25

Selling 2 half-bushels        $6.50         -26.5           702.25

Selling 3 half-bushels      $10.50         -22.50         506.25

Selling 4 half-bushels      $14.50         -18.50          342.25

Sum of squared differences                                     3,722

Mean of squared differences = 744.4 (3,722/5)

Standard deviation = square root of the mean

= 27.28

= $27.28