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Goodwill is an intangible asset related to the acquisition of one firm by another. In particular, goodwill is recognized when the purchase price exceeds the total fair values of all visible solid assets and intangible assets bought in the acquisition, as well as the liabilities, are taken in the process. Some examples of goodwill include the value of a company's brand name, a strong customer base, excellent customer relations, good staff relations, and any patents or proprietary technologies.

The selling price per pie is $ 17.99 and the cost per pie is $ 6.75.

Calculation of profit

Profit = Selling price – Cost price

Profit = $ 17.99 - $ 6.775

Profit = $ 11.24

The expected profit for 15 apple pies will be

=$ 11.24 × 15

= $ 168.60

Therefore, the expected profit from selling 15 apple pies will be $ 168.603

The cost of underestimating the demand is considered a loss of profit. calculate the cost of underestimating, as shown below:

$\begin{array}{rcl}{\mathrm{C}}_{\mathrm{u}}& =& \mathrm{Selling}\mathrm{Price}-\mathrm{Cost}\mathrm{Price}\\ & =& \$17.99-\$6.75\\ & =& \$11.24\end{array}$

The cost of overestimating the demand is considered a loss arising due to selling the particular unit at salvage value. The salvage value is $ 0.99.

Therefore, the cost of overestimating the demand becomes

$\begin{array}{rcl}{\mathrm{C}}_{\mathrm{o}}& =& \mathrm{Cost}\mathrm{price}-\mathrm{Salvage}\mathrm{value}\\ & =& \$6.75-\$0.99\\ & =& \$5.76\end{array}$

The optimal probability of not being sold, denoted by P, is calculated below:

$\begin{array}{rcl}\mathrm{P}& â‰\yen & \frac{{\mathrm{C}}_{\mathrm{u}}}{{\mathrm{C}}_{\mathrm{o}}+{\mathrm{C}}_{\mathrm{u}}}\\ & =& \frac{\$11.24}{\$11.24+\$5.76}\\ & =& 0.6612\end{array}$

To determine the corresponding number of units compute the cumulative probability.

The optimal probability of not being sold, denoted by P, is calculated below:

To determine the corresponding number of units compute the cumulative probability

From the above distribution data. The probability of 0.6612 corresponds to 20 units.

Thus, the company should take 20 units every day to maximize its expected profit.