Exercises sheet A3 
School of Mathematics 
The University of Edinburgh 
Year: 2022/2023 
Farm-co is a agricultural corporation that wants to plan their farming operations for the 
next 10 years. Farm-co owns a farm consisting of 10 blocks of land. The size of each block 
of land can be found in the table below. 
Block of land size (m2) 
1 100 
2 250 
3 500 
4 125 
5 800 
6 75 
7 900 
8 360 
9 465 
10 90 
Farm-cocanplant threedifferent crop types in theseblocks, namelygrain, beansandwheat. 
The yield, selling price and yield each food type can be found in the table below. 
crop yield (kg/m2) Sewing cost (£/ m2) Selling price £/kg 
grain 3 15 4.5 
beans 2 10 6 
wheat 3.5 12 5 
Alternately, Farm-co can also decide to purchase cattle to rear on their farm. A single cow 
takes up 5m2 and is purchased as a calf for £200 per calf. Farm-co can only purchase calf’s 
and sell all of the cows at the end of the 10 year time period. The price for selling t -year old 
cow is provided in the table below. 
Age of cow Selling price (£/ cow) 
1 350 
2 450 
3 550 
4 600 
5 700 
6 950 
7 1100 
8 1250 
9 1400 
10 1700 
1 
Additionally, in order to rear a cow, Farm-co requires 15kg of grain per cow. They can either 
use grain which was grown in the previous year or they can purchase grain at a price of £50 
per kg. Furthermore, suppose that Farm-co does not want to use more than 50% of their 
land usage for any individual activity (eg rearing cattle). 
Exercise 1Model (10 marks) 
Write a linear optimisation model that maximises Farm-co’s profits . 
Exercise 2 Solve (10 marks) 
Write a Mosel file for this model and solve the problem with Xpress. Print your results in a 
suitable format.