1) A farmer has 20 hectares for growing barley and swedes. The farmer has to decide how
much of each to grow. The cost per hectare for barley is $30 and for swedes is $20. The
farmer has budgeted $480. Barley requires 1 man-day per hectare and swedes require 2
man-days per hectare. There are 36 man-days available. The profit on barley is $100 per
hectare and on swedes is $120 per hectare. Find the number of hectares of each crop the
farmer should sow to maximize profits.
Use the following to answer the problem above:
(a) Unknowns
x = number of hectares of barley
y = number of hectares of swedes
(b) Constraints
Land x + y ≤ 20
Cost 30x + 20y ≤ 480
Manpower x + 2y ≤ 36
Apparent Constraints
x ≥ 0
y ≥ 0
(c) Profit
P = 100x + 120y