Waec Model Questions Vol1 2017 Economics Question 49

A farmer has a total cultivated area that yields 100 tonnes of produce each season, regardless of the crop mix. He can grow maize or soybeans on this land. Fixed costs per season are ₦1,200,000. Variable cost per tonne is ₦30,000 for maize and ₦45,000 for soybeans. The guaranteed market price for maize is ₦50,000 per tonne. Soybean price is uncertain: with probability 0.6 it will be ₦80,000 per tonne and with probability 0.4 it will be ₦55,000 per tonne. Let x be the proportion (0 ≤ x ≤ 1) of the total area allocated to soybeans (the remainder to maize). Determine the value of x that maximises the farmer's expected profit while ensuring that the probability of a loss (negative profit) is less than 10 %. State the optimal proportion x and the corresponding expected profit.