A corporate agricultural organization has three separate farms which are to be used during the coming year. Each farm has unique characteristics which make it most suitable for raising one crop only. Table below indicates the crop selected for each farm, the annual cost of planting 1 acre of the crop, the expected revenue to be derived from each acre, and the fixed costs associated with operating each farm. In addition to the fixed costs associated with operating each farm, there are annual fixed costs of $75,000 for the corporation as a whole.
Farm Crop Cost/Acre (cj) Revenue/Acre (rj) Fixed Cost (Fj)
1 Soya beans $900 $1,300 $150,000
2 Corn $1,100 $1,650 $175,000
3 Potatoes $750 $1,200 $125,000
Table 2
Determine the profit function for the three-farm operation.
What are the expected profits for the program if the board of directors has voted on the following planting program for the coming year; 1,000 acres will be planted at farm 1, 1,600 at farm 2 and 1,550 at farm 3?
A Summer drought has resulted in the revenue yields per acre being reduced by 20, 30 and 10 percent, respectively, at the three farms. What is the profit expected from the mentioned planting program?
Answers
Given : A corporate agricultural organization has three separate farms which are to be used during the coming year
To Find : Determine the profit function for the three-farm operation.
Solution:
Profit = Total Revenue - Variable Cost - Fixed Cost
Total Revenue = Revenue/Acre x Number of Acres
Variable Cost = Cost /Acre x Number of Acres
Total Profit = Each Profit - annual fixed costs of $75,000 for the corporation as a whole.
= Each Profit - $75,000
Farm Crop Cost Revenue Fixed Cost (Fj) Profit Function
1 Soya beans $900 $1,300 $150,000 400x - 150,000
2 Corn $1,100 $1,650 $175,000 550y - 175,000
3 Potatoes $750 $1,200 $125,000 450z - 125,000
x , y & z are acres planted in each farm respectively
x = 1000
y = 1600
z = 1550
Total Profit function = 400x - 150,000 + 550y - 175,000 + 450z - 125,000 -75,000
Profit at Farm 1 = 400*1000 - 150,000 = $ 250,000
Profit at Farm 2 = 550*1600 - 175,000 = $ 705,000
Profit at Farm 3 = 450*1550 - 125,000 = $ 572,500
Total Profit = 250,000 + 705,000 + 572,500 - 75000
Total Profit =$ 1,452,500
reduced by 20, 30 and 10 percent, respectively, at the three farms.
1000 - (20/100)1000 = 800
1600 - (30/100)1600 = 1120
1550 - (10/100)1550 = 1395
Profit at Farm 1 = 400*800 - 150,000 = $ 170,000
Profit at Farm 2 = 550*1120 - 175,000 = $ 441,000
Profit at Farm 3 = 450*1395 - 125,000 = $ 502,750
Total Profit = 170,000 + 441,000 + 502,750 - 75000
Total Profit = $ 1,038,750
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