A farmer is going to divide her 50 acre farm between two crops. Seed for crop A costs $30 per acre. Seed for crop B costs $15 per acre. The farmer can spend at most $1050 on seed. If crop B brings in a profit of $100 per acre, and crop A brings in a profit of $40 per acre, how many acres of each crop should the farmer plant to maximize her profit? solutionspile.com

Question

A farmer is going to divide her 50 acre farm between two crops. Seed for crop A costs

$30

per acre. Seed for crop B costs

$15

per acre. The farmer can spend at most

$1050

on seed. If crop B brings in a profit of

$100

per acre, and crop A brings in a profit of

$40

per acre, how many acres of each crop should the farmer plant to maximize her profit? Let

x

be the number of crop

A

and

y

be the number of crop

B

. The constraints are I.

x>=0

II.

y>=0

III.

x y<=50

IV.

30x 15y<=1050

Objective Function: Maximum Profit

=40x 100y

5258III.

x y<=50

IV.

30x 15y<=1050

Objective Function: Maximum Profit

=40x 100y

The graph of the constraints are given, find the vertices. \table[[Vertex A,Vertex B,Vertex C,Vertex D],[,

?

,,

?

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