A farmer has 150 acres of land suitable for cultivating Crops A and B. The cost of cultivating Crop A is $40/acre, and the cost of cultivating Crop B is $60/acre. The farmer has a maximum of $7400 available for land cultivation. Each acre of Crop A requires 20 labor-hours, and each acre of Crop B requires 25 labor-hours. The farmer has a maximum of 3300 labor-hours available. He has also decided that he will cultivate at least 80 acres of Crop A. If he expects to make a profit of $180/acre on Crop A and $200/acre on Crop B, how many acres of each crop should he plant to maximize his profit?

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Business

Caprice

19 June, 19:32

A farmer has 150 acres of land suitable for cultivating Crops A and B. The cost of cultivating Crop A is $40/acre, and the cost of cultivating Crop B is $60/acre. The farmer has a maximum of $7400 available for land cultivation. Each acre of Crop A requires 20 labor-hours, and each acre of Crop B requires 25 labor-hours. The farmer has a maximum of 3300 labor-hours available. He has also decided that he will cultivate at least 80 acres of Crop A. If he expects to make a profit of $180/acre on Crop A and $200/acre on Crop B, how many acres of each crop should he plant to maximize his profit?

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Maryjane Wallace · Answer 1

Cost of cultivating crop A and crop B = 40A + 60B < = 7400

Labour/hour = 20A + 25B < = 3300

Maximum profit = l80A + 200B

Explanation:

Cost of cultivating crop A< = $40/acre

Cost of cultivating crop B < = $60 / acre

The farmer has a maximum of $7400 for cultivating

Total cost = 40A + 60B < = 7400

Each acre of crop A require 20 labour - hour

Each acre of crop B require 25 ls our - hour

The farmer has a maximum of 3300 labour - hours

Total labour hour = 20A + 25 B < = 3300

If the farmer expects to make profit of $18₩/acre on crops and $200/acre on crop B,

His maximum profit P = 180A + 200B