Question

The CEO of Asempa farms limited is considering whether to plant this year’s yam with a fertilizer or go organic (i.e. without fertilizer). In case of using a fertilizer, 10kg of either the Platinum or Standard type fertilizer would be needed at the start of the planting year. The Platinum type is GH¢1000 per kilogram and could lead to a high yield of 30 tons or a moderate yield of 20 tons of yam at the end of the year. The Standard type is GH¢800 per kilogram and could also lead to a high yield of 15 tons or a moderate yield of 10 tons of yam at the end of the year. The Standard has fewer chemicals and would lead to tastier yam that sells for a higher price than that of Platinum. There is a probability of 0.7 that high yield would be recorded at the end of the year.

Market price for yam is uncertain and depends on the type as well as the volume of yam on the market. Generally, a year of high yield results in higher volume whiles a year of moderate yield leads to moderate volume of yam on the market. Even then, there is 60-40 chance that yam from the Platinum fertilizer could sell for GH¢2000 or GH¢2400 per ton in times of high yield, and GH¢3000 or GH¢3500 per ton in times of moderate yield. The Standard fertilizer yam has a 40- 60 chance of selling for GH¢4000 or GH¢5000 per ton in times of high yield, and GH¢5500 or GH¢6000 in times of moderate yield.

Organic yam would take 2 years to harvest and would require the supply of manure that can be borrowed from a local shop at a total cost of GH¢8,500 at the end of year 2. This could lead to a high yield of 8 tons or a moderate yield of 6 tons at the end of year 2. Prices for organic yam are quite high and will sell for GH¢9,000 per ton in a high yield season and GH¢11,000 in moderate yield season. Assume interest rate of 10% per year and answer the following questions.

a. Draw a decision tree for the problem faced by the CEO indicating the probabilities of occurrence and monetary values of events.

b. Advice the CEO of Asempa farms on which decision to take if he wants to make his decision based on expected monetary value technique. Show your calculations.

Answer 1

Solution:

Given

a.) Cost of the platinum fertilizer =1000/per kg

Total Cost of the platinum fertilizer =1000 * 10

=10000 GH¢

Cost of standard type=800 / per kg

Total Cost of standard type=800 * 15

=12000 GH¢

ORGANIC:- Total manure cost=15000 GH¢

Values:-

F =0.5*50000+0.5*65000= 57000 ¢

G=0.5*50000+0.5*70000=60000  ¢

D=0.6*57500+0.4*60000= 58500 ¢

E=0.6*63000+0.4*48000= 57000 ¢

B=max(D,E)=max(58500,28500)= 58500 ¢

C=0.6*65000+0.4*45000=57000 ¢ for 2 grams

=28500 ¢ for 1 gram

A=max(B,C)=max(58500,28500)=58500 ¢

b.) Since B is greater than C [BC]in terms of values CEO of asempa should choose plainum type fertilizer.

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