Accra Brewery Limited (Ghana) has to decide how to source its raw materials of wheat, maize, groundnut, and soya beans f

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Accra Brewery Limited (Ghana) has to decide how to source its
raw materials of wheat, maize, groundnut, and soya beans for its
production next quarter. It can do so through a combination of
outsourcing from other farmers or through ‘in-house’ from its own
farm of a size of 1000 acres. Based on past average yields, the
company knows an acre of land dedicated to the growing of wheat,
maize, groundnut, and soya beans would generate yields of 4, 8, 10,
and 4 tonnes respectively. The company will need at least 2800
tonnes of wheat for next quarter production but believes it might
have 300 tonnes of current inventory left to start next quarter.
Similarly, the company will need at least 3400 tonnes of maize for
next quarter production, but believes will have 400 tonnes of
current inventory left to start next quarter. Groundnut and soya
beans are substitutes (i.e., one can be used in place of another)
and in total will need at least 6000 tonnes. For strategic
purposes, the company has the policy that the total tonnes of all
four raw materials outsourced from other farmers must not exceed
the total tonnes of all four raw materials obtained in-house (i.e.,
from its farm). Also, due to government regulations, the total
yield of maize from the company’s farm cannot exceed 2100 tonnes.
In-house farming would require the use of a fertilizer of which the
company has available 5000 litres. An acre of wheat, maize,
groundnut, and soya beans will require 4, 3, 5, and 2 litres of
fertilizer between planting and harvesting. The planting cost per
acre are GHS2280, GHS3300, GHS4080, and GHS2160 for wheat, maize,
groundnut, and soya beans respectively. Also, a tonne of wheat,
maize, groundnut, and soya beans cost GHS600, GHS420, GHS450, and
GHS570, respectively when outsourced from other farmers. (a) Define
the decision variables for this problem (b) Provide a linear
programming formulation to help the company minimize the cost of
sourcing its raw materials for next quarter production. (c) Solve
the LP model of Accra Brewery Limited (Ghana) using MS Excel Solver
and use your report to answer the following questions. (i) What is
the advice the company should follow (in terms of the decision
variables) given the output of the model, and what will be the
total cost if this advice is taken? (ii) The report indicates that
the company should use groundnut in place of soya beans. Why is
this so, and what should be the price of soya beans from other
farmers to attract the company to consider outsourcing soya beans?
(iii) Will the advice change if the cost of maize when outsourced
reduces by GHS15? Explain. (iv) How many tonnes of wheat, and
groundnut were obtained through in-house farming? (v) What is your
interpretation of the dual value of land? (vi) Why is the shadow
price for the availability of Fertilizer zero