A farm occupies 200 acres of land and has £10000 available for investment. The family whorun the farm can work for a total of 5000 work-hours during the winter and 7000 work-hoursfor the rest of the year. If any of these work-hours are not needed then the family will usethem to help at the local village store, earning a profit of £9 per hour (regardless of the timeof year). Past experience shows the family will not have more than 50 spare work-hours towork in the village store during the winter and not more than 80 over the summer.The farm brings in cash for the family from three crops (lettuces, carrots, and swedes) andtwo types of livestock (dairy cows and hens). The family would like to maximise their cashincome. The crops need no investment funds but each cow requires an initial investment of£1000 and each hen £10. Each cow needs 1.5 acres of land and the size of the barn limits thenumber of cows in the herd to 20. Each cow also require 100 work hours during the winterand 60 hours during the rest of the year. The hens do not need any specific land, but the farmcan accommodate a maximum of 100 hens. To look after them well, each hen needs 1.1work hours during the winter and 0.8 work hours during the rest of the year. A cow bringsin a net annual income of £400 while a hen generates £3.Crops also generate income and require work hours to tend to them. The table below sum-marises such information:crop winter work hours summer work hoursLettuceCarrotsSwede202510104010income (per acre)£100£130£110Formulate this scenario as a linear programming problem, making sure you clearly and fullydefine your decision variables, constraints, and objective function.

Let x be the number of cows, y be the number of hens, l be the number of acres for lettuce, c be the…

Answered: Formulate this scenario as a linear…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Formulate this scenario as a linear programming problem, making sure you clearly and fully define your decision variables, constraints, and objective function.