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日期：2022-11-05 08:49

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)

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)

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.