(Chemical Manufacturing) A chemical manufacturer produces a certain chemical compound every Sunday, which it then sells to its customers on Monday through Saturday. The company earns a revenue of $80 per kg of the compound sold. Each kg manufactured costs the company $40. If any of the compound goes unsold by Saturday night, it must be destroyed safely, at a cost of $15 per kg. The total demand for the chemical compound throughout the week has a normal distribution with a mean of 260 kg and a standard deviation of 80 kg.a) How much of the chemical compound should the company produce every Sunday?b) What is the expected cost (including manufacturing cost, lost profit, and disposal cost) per week?

Earn revenue per kg = $40 (that is often recognized as the expenses) and the sum of the company would not be allowed if the consumer has no kg of the product.

Overstocking cost in per kg = $40 production cost + $15 disposal cost

= $55

the corporate amount should be borne if additionals kg is generated.

In potion A:

Due to regular transfer, the optimal quantity of data must not be generated per week = [tex]\mu +Z\times \sigma[/tex] ([tex]\mu[/tex]= average demand, Z = normal distribution score, and [tex]\sigma[/tex] = standard deviation).

[tex]Z =\frac{\ Understocking \ Cost}{\ Understocking \ Cost +\ Overstocking \ Cost}[/tex]

Each Saturday the company of chemicals composites shall produce = 244

In potion B:

Weekly estimated cost

[tex]= \text{Maximum weekly order (244 kg)} \times \ Production \ overhead \ per \ kg (\$ 40)}\\[/tex]

[tex]= \$ 9,760[/tex]