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# Time projections and tables

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Three individual steps to be taken before the service could begin: (1) write instructions and procedures, (2) select techniques to operate the equipment, and (3) procure the equipment. It would be possible to save time on the project, by paying some premiums to complete certain activities faster than the normal schedule listed below.
If the equipment were shipped by express truck, one week could be saved. Air freight would save two weeks. However, a premium of \$200 would be paid for the express truck shipment and \$750 would be paid for air shipment. The operator training period could also be reduced by one week if the trainees worked overtime. However, this would cost the facility an additional \$600. The time required to complete the instructions could be reduced by one week with the additional expenditure of \$400. However, \$300 could be saved if this activity was allowed to take three weeks

What is the shortest time period in which the project can be completed using the expected times listed in the table above.

What is the shortest time in which the project can be completed if extra money is used to reduce the times for certain activities?

What is the lowest cost schedule for this shortest time?

Table is attached.

https://brainmass.com/math/computing-values-of-functions/time-projections-tables-448261

#### Solution Summary

Time projections and tables are examined. The lowest cost schedule for the shortest time is examined.

\$2.19
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## Probabilities & Decision Making for a Winery

I need help with the following question set:
A winery purchased land for establishing a new vineyard. Management is considering 2 varieties of white grapes for the vineyard: Chardonnay & Riesling. The Char. grapes would be used to make a dry wine and the Riesling grapes would be for a semi-dry Riesling wine. It takes almost 4 yrs from the time of planting before new grapes can be harvested. This length in time creates a great amount of uncertainty about future demands and makes the decision concerning the type of grapes to plant difficult. 3 possibilities are being considered: Char. grapes only, Riesling grapes only, & both types of grapes. The management decided that for planning purposes it would be adequate to consider only 2 demand possibilities for each type of wine: Strong or weak. With 2 possibilities for each type of wine it was necessary to assess 4 probabilities. With some forecasts in industry publications, management made the following assessments.

Riesling Demand
Char. Demand Weak Strong

Weak 0.05 0.5
Strong 0.25 0.2

Revenue projections show an annual contribution to profit of \$20,000 if the winery only plants Char. grapes and demand is weak for Char. wine and \$70,000 if they only plant Char. grapes and demand is strong for Char. wine. If they only plant Riesling grapes, the annual profit projection is \$25,000 if demand is weak for Riesling grapes and \$45,000 if demand is strong for Riesling grapes. If the winery plants both grapes, the annual profit projections are shown in the following table.

Riesling Demand
Char. Demand Weak Strong

Weak \$22,000 \$40,000
Strong \$26,000 \$60,000

a. What decision should be made, what is the chance event & what is the consequence? Identify alternatives for the decisions & possible outcomes for the chance events.

b. Develop a decision tree

c. Use expected value approach to recommend which alternative the winery should follow in order to maximize expected annual profit.

d. Suppose mgmt is concerned about probability assessments when demand is strong for Char. Wine. Some believe the demand for Riesling wine to also be strong. Suppose the probability of strong demand for Char. & weak demand for Riesling is 0.05 & that the probability if strong demand for Char and strong demand for Riesling is 0.40. How does this change the recommended decision? Assume the probabilities when Char. demand is weak are still 0.05 & 0.50.

e. Some management members expect the Char. market to become saturated at some point in the future causing a fall in prices. Suppose that the annual project projections fall to \$50,000 when demand for Char. is strong & Char. grapes only are planted. Using the original probability assessments, determine how this change would affect the optimal decision.
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