Flora Wei owns a 300 acre farm near Scarborough. She is planning the operations of her farm for the coming year. She has $200,000 available for investment during the coming year, and she estimates that she has 1500 labour hours available for Fall/Winter months (October-March), and 5000 labour hours available for the Spring/Summer months (April-September). If any of these labour hours are not required, they may be used in working at local farmers' cooperative, at a rate of $16.35 per hour during the Fall/Winter months and $17.50 per hour during the Spring/Summer months. Flora obtains income from the production of wheat, soybeans, peaches, cows, lambs and providing unused labour hours to local farmers' cooperative. Her estimates of the labour hour requirement, annual income, and annual investment per acre from three crops are as follows: Wheat Soybeans Peaches Fall/Winter Labour hr. requirement/acre 20 15 not grown Spring/Summer Labour hr. requirement/acre 40 45 50 Annual income/acre $1700 $1650 $1800 Annual investment/acre $140 $120 110 The corresponding estimates for the two types of livestock are as follows. Cows Lambs Fall/Winter Labour hr. requirement/head 15 5 Spring/Summer Labour hr. requirement/head 10 4 Annual Investment/head $350 $120 Annual income/head $650 $225 Additionally, Flora estimates that each cow raised require 0.25 acres of land, and each lamb 0.15 acres of land. She would like to limit her cow herd to a maximum of 200 cows a year and lamb herd to a minimum of 400 lambs a year. She wants her investment in cows and lambs to be not more than 40% of the total investment, and she wants lamb herd to be at least twice as big as cow herd. Formulate the linear programming model for Flora Wei's farm operations planning problem.