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Question

A fruit grower has 150 acres of land available to raise two crops, A and B. It takes one day to trim an acre of crop A and two days to trim an acre of crop B, and there are 240 days per year available for trimming. It takes 0.3 day to pick an acre of crop A and 0.1 day to pick an acre of crop B, and there are 30 days per year available for picking. Fruit grower planted the crops in order to maximize his profit, then his maximum profit is (assuming that the profit is 140 per acre for crop A and 235 per acre for crop B)

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Solution

The correct option is **C** 29550

let x = number of acres of crop A.

let y = number of acres of crop B.

the equation we want to maximize is the profit equation.

the profit on crop A is 140 per acre so the total profit on crop A would be:

140x

the profit on crop B is 235 per acre so the total profit on crop B would be:

235y

it takes 1 day to trim an acre of crop A and 2 days to trim an acre of crop B with a total of 240 days available for trimming.

1×x+2×y≤240

Also, .3 day to pick an acre of crop A and .1 day to pick an acre of crop B with a total of 30 days available for picking.

3x+y≤300

total number of acres has to be less than or equal to 150.

x+y≤150

So, constraints are:

x+y≤150, 3x+y≤300, x+2y≤240, x, y≥0

Now, As we have values of z

let x = number of acres of crop A.

let y = number of acres of crop B.

the equation we want to maximize is the profit equation.

the profit on crop A is 140 per acre so the total profit on crop A would be:

140x

the profit on crop B is 235 per acre so the total profit on crop B would be:

235y

it takes 1 day to trim an acre of crop A and 2 days to trim an acre of crop B with a total of 240 days available for trimming.

1×x+2×y≤240

Also, .3 day to pick an acre of crop A and .1 day to pick an acre of crop B with a total of 30 days available for picking.

3x+y≤300

total number of acres has to be less than or equal to 150.

x+y≤150

So, constraints are:

x+y≤150, 3x+y≤300, x+2y≤240, x, y≥0

Now, As we have values of z

Corner Points | z=140x+235y |

(60,90) | 29550(maximum) |

(75,75) | 28125 |

(0,120) | 28200 |

(100,0) | 14000 |

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