Agri Farm Ventures produces cases of food products. Each case contains an assortment of fruits, vegetables, and other fresh produce. Each case costs $5 and sells for $15. If there are any cases not sold by the end of the day, these are sold to another company for $3 a case to process. The probability that the daily demand will be 100 cases is 0.3, the probability that daily demand will be 200 cases is 0.4, and the probability that daily demand will be 300 cases is 0.3. Agri Farm Ventures has a policy of making sure customers are always satisfied. Hence, if its own supply of cases of food products is less than the demand, it buys the necessary products from a competitor. The estimated cost of doing this is $16 per case. Question 1 1 pts Refer to the Agri Farm Ventures problem. What are the decision alternatives

We need to calculated the expected return for each scenario

Probability of 100 cases sold

(100*15) - (100*5) = $1000

200 cases there is also a possibility that supply will be greater than the demand so the case will be sold to competitor so 100 cases bought from competitor at $16 cost and sold for $15

[ (100*$15) - (100*$5) ] + [ (100*$16) - (100*$15) = $900

300 cases there is also a possibility that supply will be greater than the demand so the case will be sold to competitor so 200 cases bought from competitor at $16 cost and sold for $15

[ (100*$15) - (100*$5) ]+[ (200*$16) - (200*$15) ]=$800

Then calculate the probabilites of each to see the decisions

$1000*0.3=$300

$900*0.4=$360

$800*0.3=$240

Answer: (1) They should be producing 300 cases each day because it result in the highest EMV of $1,800 (2) The cases that are not sold by the end of the day should be sold to another company to process in order to reduce their loss (3) When their own supply is less than demand they should buy necessary products from a competitor in order to ensure that they do not lose their customers.

Explanation:

We compute a decision table to solve the question as follows

When demand is 100 cases

At decision table

100 = (100 * 15) - (100 * 5)

=1,500 - 500

=1,000

At decision table

200 = (100*15) - (100*5) - (100*16) - (100*15)

= (1,500 - 500) - (1,600 - 1,500)

=1,000 - 100

=900

At decision table

300 = (100 * 15) - (100 * 5) - (200 * 16) - (200 * 15)

= (1,500 - 500) - (3,200 - 3,000)

= 1,000 - 200

=800

EMV when demand is 100 cases

= 0.3 (1000) + 0.4 (900) + 0.3 (800)

=300 + 360 + 240

=900

When demand is 200 cases

At decision table

100 = (100 * 15) - (200 * 5) + (100 * 3)

= (1,500 - 1000) + 300

=500 + 300

= 800

At decision table

200 = (200 * 15) - (200 * 5)

= 3,000 - 1,000

= 2,000

At decision table

300 = (200 * 15) - (200 * 5) - (100 * 16) - (100 * 15)

= (3,000 - 1,000) - (1,600 - 1,500)

= 2,000 - 100

= 1,900

EMV when demand is 200 cases

0.3 (800) + 0.4 (2,000) + 0.3 (1,900)

=240 + 800 + 570

= 1,610

When demand is 300 cases

At decision table

100 = (100 * 15) - (300 * 5) + (200 * 3)

= (1,500 - 1,500) + (600)

= 0 + 600

= 600

At decision table

200 = (200 * 15) - (300 * 5) + (100 * 3)

= (3,000 - 1,500) + (300)

= 1,500 + 300

= 1,800

At decision table

300 = (300 * 15) - (300 * 5)

= (4,500 - 1,500)

= 3,000

EMV when demand is 300

0.3 (600) + 0.4 (1,800) + 0.3 (3,000)

= 180 + 720 + 900

=1,800

The decision alternatives based on the decision table is that

(1) They should be producing 300 cases each day because it result in the highest EMV of $1,800

(2) The cases that are not sold by the end of the day should be sold to another company to process in order to reduce their loss

(3) When their own supply is less than demand they should buy from competitors in order to ensure that they do not lose their customers