#### Description

##### Coren Chemical, Inc., develops industrial chemicals...

Description

Question

Coren Chemical, Inc., develops industrial chemicals
that are used by other manufacturers to produce photographic
chemicals, preservatives, and lubricants.
One of their products, K-1000, is used by several
photographic companies to make a chemical that is
used in the film-developing process. To produce
K-1000 efficiently, Coren Chemical uses the batch
approach, in which a certain number of gallons is
produced at one time. This reduces setup costs and
allows Coren Chemical to produce K-1000 at a competitive
price. Unfortunately, K-1000 has a very
short shelf life of about one month.
Coren Chemical produces K-1000 in batches
of 500 gallons, 1,000 gallons, 1,500 gallons, and
2,000 gallons. Using historical data, David Coren
was able to determine that the probability of selling
500 gallons of K-1000 is 0.2. The probabilities of
selling 1,000, 1,500, and 2,000 gallons are 0.3, 0.4
and 0.1, respectively. The question facing David ishow many gallons to produce of K-1000 in the next
batch run. K-1000 sells for \$20 per gallon. Manufacturing
cost is \$12 per gallon, and handling costs and
warehousing costs are estimated to be \$1 per gallon.
In the past, David has allocated advertising costs to
K-1000 at \$3 per gallon. If K-1000 is not sold after
the batch run, the chemical loses much of its important
properties as a developer. It can, however, be
sold at a salvage value of \$13 per gallon. Furthermore
David has guaranteed to his suppliers that
there will always be an adequate supply of K-1000.
If David does run out, he has agreed to purchase a
comparable chemical from a competitor at \$25 per
gallon. David sells all of the chemical at \$20 per gallon
so his shortage means that David loses the \$5 to