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25 Marks Question 2 Jabulani Modise operates a 100 -hectare farm in the prime farming region of Ventersdorp. He is currently busy with the planning of the next farming season and has approached you for assistance based on a tip by his son who is your university friend in the Faculty of Agriculture. He has promised you a reasonable reward for your efforts. The farm always grows wheat and sunflower each season and always must comply with the government quota (allocation) system which requires at least 30 hectares of wheat and 20 hectares of sunflower for each season to be planted and harvested. A hectare typically yields 8 tons of wheat and 10 tons of sunflowers, a ton of wheat sells for N\$2 500 and a ton of sunflower sells for N\$2 200. Each hectare of wheat requires 2 tons of fertilizer which is sourced at N\$80 per 50kg bag. Sunflower requires 2,5 tons of fertilizer which costs N$120 per 100kg bag. Both crops are sprayed by a pesticide called Fenvalerate, the ideal spray is 100 litres per hectare of wheat and 150 litres per hectare of sunflower. In large quantities, this pesticide is harmful to birds, as such, the government only allows a maximum of 9000 litres to be used at farms of Mr Modise's size. A litre of the pesticide costs N\$40 A hectare of wheat requires 480 labour minutes and sunflower requires 300 minutes. The cost per direct labour hour is N\$400. A total of 42000 minutes is available for the farming season. All other variable costs are N\$3 000 per hectare of wheat and N\$4000 per hectare of sunflower. Fixed costs allocated for a hectare of wheat is N\$1 500 and sunflower hectare is N\$1 800 respectively. Required: 2.1. Use the graphical method and determine the combination of hectares of wheat and sunflower to maximise contribution. Indicate the feasible region on a graph and calculate the profit at each of the extreme points. 20 Marks 2.2. Based on your answer in (2.1) above, compute the shadow price of a litre of pesticide at the optimal combination of wheat and sunflower. 5 Marks Note: Round un to the nearest whole number e.g., 30.5 becomes 31

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