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 beliefs 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 fertilizer of which the company has available 5000 liters. An acre of wheat, maize, groundnut, and soya beans will require 4, 3, 5, and 2 liters of fertilizer between planting and harvesting. The planting cost per acre is 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.

1. 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?
2. 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?
3. Will the advice change if the cost of maize when outsourced reduces by GHS15? Explain.
4. How many tonnes of wheat, and groundnut were obtained through in-house farming?
5. What is your interpretation of the dual value of land?
6. Why is the shadow price for the availability of Fertilizer zero?