Question

A farmer has 1,170 acres of land on which he grows corn, wheat, and soybeans. It costs $45 per acre to grow corn, $60 to grow wheat, and $50 to grow soybeans. Because of market demand the farmer will grow twice as many acres of wheat as of corn. He has allocated $62,250 for the cost of growing his crops. How many acres of each crop should he plant?

a. corn acres
b. wheat acres
c. soybeans acres

Answer 1

Answer:

Corn Land = 250 Acres ; Wheat Land = 500 Acres ; Soybean Land = 420 Acres

Step-by-step explanation:

Let the number of acres allocated to corn = c

So, no. of acres allocated to wheat = twice of corn = 2c

Total land for farming  = 1170 acres

So, soybean allocated acres = 1170 - c - 2c = 1170 - 3c

Total Cost =  Σ [Cost per acre of each crop x No. of Acres allocated to it ]

62250 = 45c + 60 (2c) + 50 (1170 - 3c)

62250 = 45c + 120c + 58500 - 150c

62250 - 58500 = 15c

3750 = 15c

c = 3750 / 15

c = 250 [Corn Allocated Land]

Wheat allocated land = 2c = 2 (250) = 500

Soybean allocated land = 1170 - 3c = 1170 - 3 (250) = 1170 - 750 = 420

Answer 2

The allocated acres for the 3 crops are;

A) Corn acres = 250 acres

B) Wheat acres = 500 acres

C) soybean acres = 420 acres

Let the number of acres allocated to corn = c

We are told that he grows twice as many acres of wheat as corn. Thus;

number of acres allocated to wheat = 2c

Total are of land for farming = 1170 acres

Thus;

Number of acres allocated to soyabean = 1170 - (c + 2c) = 1170 - 3c

We are given the total cost for growing his crops to be $62,250. Thus;

62250 = Σ(Cost per acre of each crop x No. of Acres allocated to it)

Cost per acre of corn = $45

Cost per acre of wheat = $60

Cost per acre of soybean = $50

Thus;

62250 = 45c + 60(2c) + 50(1170 - 3c)

62250 = 45c + 120c + 58500 - 150c

62250 - 58500 = 15c

3750 = 15c

c = 3750 / 15

c = 250 acres

Thus;

Allocated acres for wheat = 2c = 2(250) = 500 acres

Allocated acres for soyabean = 1170 - 3c

>> 1170 - 3 (250)

>> 1170 - 750 = 420 acres

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