QUESTION ONE (a) The Uganda Farmers Research Institute suggested to a farmer to spread out at...

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QUESTION ONE (a) The Uganda Farmers Research Institute suggested to a farmer to spread out at least 4800 kg of a special phosphate fertilizer and not less than 7200 kg of a nitrogen fertilizer to raise productivity of crops in his fields. There are two sources for obtaining these mixtures A and B. Both of these are available in bags weighing 100 kg each and they cost Sh. 40 and Sh 24 respectively. Mixture A contains phosphate and nitrogen equivalent of 20 kg and 80 kg respectively, while mixture B contains these ingredients equivalent of 50 kg each. Determine how many bags of each type the farmer should buy in order to obtain the required fertilizer at minimum cost. (7 marks) (b) Given that 6 7 -1 Q= 3 n 5 9 11 n Where Q is non-invertible matrix, determine the value of n? QUESTION TWO (3 marks) Three companies Benfel Ltd, Cromwell Ltd and Samtec Ltd were recently launched in the Kenyan market. The companies have operated in the Kenyan market for a few months now. At the beginning of the month of August 2019, a survey on monthly brand switching behavior was conducted on a representative sample among customers of the three companies. The survey revealed that Benfel Ltd retains 70% of its customers and loses 20% to Cromwell Ltd and 10% to Samtec Ltd. Similarly, Cromwell Ltd retains 60% of its customers and loses 30% to Benfel Ltd and 10% to Samtec Ltd. Furthermore, Samtec Ltd retains 50% while it loses 30% to Cromwell Ltd and 20% to Benfel Ltd. It has been determined that there will be 3,500, 4,300 and 2,200 customers shopping with Benfel Ltd, Cromwell Ltd and Samtec Ltd respectively at the start of the month of September 2019. Evaluate the distribution of the sample surveyed as at the beginning month i. (5 marks) ii. (5 marks) of August 2019. Compare the long run state of the market amongst the three companies. QUESTION ONE (a) The Uganda Farmers Research Institute suggested to a farmer to spread out at least 4800 kg of a special phosphate fertilizer and not less than 7200 kg of a nitrogen fertilizer to raise productivity of crops in his fields. There are two sources for obtaining these mixtures A and B. Both of these are available in bags weighing 100 kg each and they cost Sh. 40 and Sh 24 respectively. Mixture A contains phosphate and nitrogen equivalent of 20 kg and 80 kg respectively, while mixture B contains these ingredients equivalent of 50 kg each. Determine how many bags of each type the farmer should buy in order to obtain the required fertilizer at minimum cost. (7 marks) (b) Given that 6 7 -1 Q= 3 n 5 9 11 n Where Q is non-invertible matrix, determine the value of n? QUESTION TWO (3 marks) Three companies Benfel Ltd, Cromwell Ltd and Samtec Ltd were recently launched in the Kenyan market. The companies have operated in the Kenyan market for a few months now. At the beginning of the month of August 2019, a survey on monthly brand switching behavior was conducted on a representative sample among customers of the three companies. The survey revealed that Benfel Ltd retains 70% of its customers and loses 20% to Cromwell Ltd and 10% to Samtec Ltd. Similarly, Cromwell Ltd retains 60% of its customers and loses 30% to Benfel Ltd and 10% to Samtec Ltd. Furthermore, Samtec Ltd retains 50% while it loses 30% to Cromwell Ltd and 20% to Benfel Ltd. It has been determined that there will be 3,500, 4,300 and 2,200 customers shopping with Benfel Ltd, Cromwell Ltd and Samtec Ltd respectively at the start of the month of September 2019. Evaluate the distribution of the sample surveyed as at the beginning month i. (5 marks) ii. (5 marks) of August 2019. Compare the long run state of the market amongst the three companies.