Palmer Jam Company is a small manufacturer of several different jam products. On

Question

Palmer Jam Company is a small manufacturer of several different jam products. One product is an organic jam that has no preservatives, sold to retail outlets. Susan Palmer must decide how many cases of jam to manufacture each month. The probability that demand will be

55

cases is

0.100.10,

for

66

cases it is

0.250.25,

for

77

cases it is

0.500.50,

and for

88

cases it is

0.150.15.

The cost of every case is

$ 45$45,

and the price Susan gets for each case is

$ 90$90.

Unfortunately, any cases not sold by the end of the month are of no value as a result of spoilage.

Based on the given information, Susan's conditional profits table for jam is:

Demand

55

66

77

88

Produce

pequals=0.100.10

pequals=0.250.25

pequals=0.500.50

pequals=0.150.15

Demand

55

cases

66

cases

77

cases

88

cases

Produce

pequals=0.100.10

pequals=0.250.25

pequals=0.500.50

pequals=0.150.15

Explanation / Answer

The cost of every case is $45

and the price Susan gets for each case is $90

Profit for each case = $90 - $45 = $45

Loss due to spoilage = 0 - $45 = -$45

When the Produce = 55 cases, in each demand = 55, 66, 77 and 88 cases, there will only be 55 cases sold.

Conditional profits = 0.1 * 55 * $45 + 0.25 * 55 * $45 + 0.5 * 55 * $45 + 0.15 * 55 * $45 = $2475

When the Produce = 66 cases,

For demand = 55 cases, there will be 55 cases sold and 11 cases unsold.

For demand = 66 cases, there will be 66 cases sold and 0 cases unsold.

For demand = 77 cases, there will be 66 cases sold and 0 cases unsold.

For demand = 88 cases, there will be 66 cases sold and 0 cases unsold.

Conditional profits = 0.1 * (55 * $45 - 11 * $45) + 0.25 * (66 * $45) + 0.5 * (66 * $45) + 0.15 * (66 * $45) = $2871

When the Produce = 77 cases

For demand = 55 cases, there will be 55 cases sold and 22 cases unsold.

For demand = 66 cases, there will be 66 cases sold and 11 cases unsold.

For demand = 77 cases, there will be 77 cases sold and 0 cases unsold.

For demand = 88 cases, there will be 77 cases sold and 0 cases unsold.

Conditional profits = 0.1 * (55 * $45 - 22 * $45) + 0.25 * (66 * $45 - 11 * $45) + 0.5 * (77 * $45) + 0.15 * (77 * $45)  = $3019.5

When the Produce = 88 cases

For demand = 55 cases, there will be 55 cases sold and 33 cases unsold.

For demand = 66 cases, there will be 66 cases sold and 22 cases unsold.

For demand = 77 cases, there will be 77 cases sold and 11 cases unsold.

For demand = 88 cases, there will be 88 cases sold and 0 cases unsold.

Conditional profits = 0.1 * (55 * $45 - 33 * $45) + 0.25 * (66 * $45 - 22 * $45) + 0.5 * (77 * $45 - 11 * $45) + 0.15 * (88 * $45)  = $2673

So, Susan's conditional profits table for jam is

Produce/Demand 55 cases 66 cases 77 cases 88 cases p = 0.10 p=0.25 p=0.50 p=0.15 Profit $2475 $2871 $3019.5 $2673

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