JM operates a 100-hectare farm in the prime farming region of Grootfontein. JM is currently busy with

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Question:

JM operates a 100-hectare farm in the prime farming region of Grootfontein. JM 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 college 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 has to 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 ton of fertilizer which if 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 9 000 litres to be used at farms of JM’s size. A litre of the pesticide costs N$40. A hectare of wheat requires 8 labour hours and sunflower requires 5 hours. The cost per direct labour hour is N$400. A total of 700 hours are available for the farming season. All other variable costs are N$3 000 per hectare of wheat and N$4 000 per hectare of sunflower.

REQUIRED: MARKS 3.1 Use the algebraic method and determine the combination of hectares of wheat and sunflower in order to maximise contribution. Indicate the feasible region on a graph, and calculate the profit at each of the extreme points. 20 3.2 Based on your answer in (3.1) above, compute the shadow price of a litre of pesticide at the optimal combination wheat and sunflower