Lecture 8: LP in Excel (Review Assign. 1) AGEC 352 Spring 2011 – February 14 R. Keeney

The 3 Crop Problem

Excel Setup of 3 Crop Problem (Show Formulas) Note the use of absolute cell references (e.g. $B$3), which allows copying of the formulas down the LHS column.

Question 1: Why split up the labor? When given a question like this, you should always feel free to solve the model again as part of you answer. VariableLabor Separated Labor Combined Profits18,31521,200 Corn planted Wheat planted Oats planted1050 Labor used (total)3, Labor used (J-A)1,600??

Question 1: Labor modeling The model without the labor split would have us overplanting corn relative to seasonal labor availability. That model also shows us that if we could move labor around in time or get more than 1600 hours in Jan-Apr we could earn more profits.

Questions 2-4. Planting ◦ Corn = 275 ◦ Wheat = 120 ◦ Oats = 105 Profits = 18,315 Binding Constraints (LHS = RHS) ◦ Total Land (500) ◦ Wheat allotment (120) ◦ Jan-Apr labor (1600)

Q4: Binding Constraints Why do we identify these? 1) While all of the constraints are part of the problem, only the constraints that bind are meaningful. ◦ They define the corner point of the solution. 2) Having more of the resource in a binding constraint would make us better off. ◦ Without solving the model you can say that removing wheat allotment will increase profits. Solve the model to know how much…

Questions 5 and 6: More land and what is it worth? Solve the model again assuming we have 501 acres of total land. ◦ Corn = ◦ Wheat = 120 ◦ Oats =  Increase oats by 1.25 while reducing corn by 0.25  Add’l land lets us use more of our labor Same constraints bind Profits = ◦ – = ~14.00 is the maximum amount of rent that can be paid for land.

Question 7: No wheat allotment Constraint binds so we know profits should increase ◦ Only reason we produce oats is the wheat allotment VariableWheat Allotment No Wheat Allotment Profits18,31519,575 Corn planted275 Wheat planted Oats planted1050 Cost of the wheat program 19,575 – 18,315 =1,260

Question 8: Corn Only Set Corn to its max value and compare ◦ The value of the crop mix is that we use resources more fully… VariableOptimal PlanCorn Only Plan Profits18,31514,400 Corn planted Wheat planted1200 Oats planted1050 Binding ConstraintsLand, Wheat Allotment, Jan-Apr Labor Jan-Apr Labor Return to Crop Mix 18,315 – 14,400 =3,915

Time for Quiz