You have a number of crop and livestock enterprises that you could produce on your farm operation.These include the following.

Crops - corn, grain sorghum, wheat, alfalfa hay, and sunflowers

Livestock - Beef cow/calf, ewe flock, dairy herd, and stocker steers

You have the following resources available to you on your farm.

• Land
  • 4,000 acres that could be used for any enterprise
  • 1,500 acres that can only be used for pasture
• Buildings & Machinery
  • Adequate for any plan that you might develop
• Labor
  • 12,500 hours available
• Feed
  • All corn and hay that is fed to livestock must be produced on the farm

You have developed an enterprise budget for each potential enterprise and you want to use that to construct a whole farm budget. The enterprise budgets show the following gross margins for each unit of each enterprise. (Units are in acres for each crop enterprise and head of animals for livestock.)

Enterprise	Gross Margin
Corn	$270.00
Sorghum	$210.00
Wheat	$195.00
Hay	$220.00
Sunflowers	$180.00
Beef	$230.00
Ewes	$110.00
Dairy	$1,690.00
Steers	$410.00

In that process of developing a whole farm budget, you have to select the enterprises that you will produce. Fortunately for you, you learned how to develop a linear programming (LP) model to help with this decision. That model is being used to maximize your farm's Gross Margin.

Your model shows the following results.

Enterprise	Optimum Level	Reduced Cost		Item	Level of Use	Slack (unused)	Shadow Price
Corn	0	-$34.26		Labor	11,900	600	$0.00
Sorghum	1,350	0		Crop Land	4,000	0	$169.84
Wheat	0	-$15.75		Pasture	1,000	0	$162.80
Hay	600	0
Sunflowers	2,050	0
Beef	296	0
Ewes	0	-$30.98
Dairy	200	0
Steers	0	-$27.08

1. Armed with your results, calculate the total gross margin for each of the 9 possible enterprises in the optimal solution. (Show your calculation for each enterprise.) What is the total gross margin for the farm, then?

Enterprise	Total Gross Margin in Optimal Solution
Corn	270.000*0= 0.00
Sorghum	210.00*1,350= 283,500.00
Wheat	195.00*0= 0.00
Hay	220.00*600= 132,000.00
Sunflowers	180.00*2,050= 369,000.00
Beef	230.00*296= 69,080.00
Ewes	110.00*0= 0.00
Dairy	1,690.00*200= 338,000.00
Steers	410.00*0= 0.00
Total Farm Gross Margin	0.00 (Corn) + 283,500.00 (Sorghum) + 0.00 (Wheat) + 132,000.00 (Hay) + 369,000.00 (Sunflowers) + 68,080.00 (Beef) + 0.00 (Ewes) + 338,000.00 (Dairy) + 0.00 (Steers) Total Farm Gross Margin = 1,190,580.00

2. By how much would gross margin change if you had one extra hour of labor to contribute to the farm business?

3. By how much would gross margin change if you forced one steer into your optimal plan? Would gross margin increase or decrease?