BPO Services is in the business of digitizing information from forms that are filled out by hand. In 2006, a big client gave BPO a distribution of the forms that it digitized in house last year, and BPO estimated how much it would cost to digitize each form. Form Type Mix of Forms Form Cost A 0.5 $3.75 B 0.5 $1.25 The expected cost of digitizing a form is $ . Suppose the client and BPO agree to a deal, whereby the client pays BPO to digitize forms. The price of each form processed is equal to the expected cost of the form that you calculated in the previous part of the problem. Suppose that after the agreement, the client sends only forms of type A. The expected digitization cost per form of the forms sent by the client is $ . This leads to an expected loss of $ per form for BPO. (Hint: Do not round your answers. Enter the loss as a positive number.)

a. The expected cost of digitizing a form is $2.50

b. The expected digitization cost per form of the forms sent by the client is $3.75, without a mix of forms.

c. This leads to an expected loss of $1.25 per form for BPO.

Explanation:

1. Data:

Form Type    Mix of Forms        Form Cost

A                       0.5                     $3.75

B                        0.5                     $1.25

b. Calculation of Expected Cost of digitizing a form:

Form Type    Mix of Forms        Form Cost    Expected Cost

A                       0.5                     $3.75             $1.875 (0.5 * $3.75)

B                        0.5                     $1.25             $0.625 (0.5 * $1.25)

Total expected costs                                        $2.50

c. Calculation of Expected cost of Form actually sent by Client without a mix of forms:

A                       01                     $3.75             $3.75 (1 * $3.75)

Total expected costs                                      $3.75

d. Calculation of Expected Loss:

Expected Price = $2.50

Expected cost =   $3.75

Expected loss =  $1.25

e. The expected value (cost, price, or gain or loss) from the form digitization is the sum of all possible values from the mix of forms, each multiplied by the probability of its occurrence.