15. A farmer can plant a combination of twodifferent crops on 20 acres of land.

Question

15. A farmer can plant a combination of twodifferent crops on 20 acres of land. Seed costs $120 per acre forcrop A and $200 per for crop B. Government restrictions limitacreage of crop A to 15 acres, but do not limit crop B. Crop A willtake 15 hours of labor per acre at a cost of $5.60 per hour, andcrop B will require 10 hours of labor per acre at $5.00 per hour.If the expected income from crop A is $600 per acre and from crop Bis $520 per acre, how many acres of crop A should be planted inorder to maximize profit?

A. 5 acres

B. 20 acres

C. 15 acres

D. infeasible

Explanation / Answer

15. A farmer can plant a combination of twodifferent crops on 20 acres of land. Seed costs $120 per acrefor

crop A and $200 per for crop B. Governmentrestrictions limit acreage of crop A to 15 acres, but do not limitcrop B.

Crop A will take 15 hours of labor per acre at acost of $5.60 per hour, and crop B will require 10 hours of laborper

acre at $5.00 per hour. If the expected incomefrom crop A is $600 per acre and from crop B is $520 peracre,

how many acres of crop A should be planted inorder to maximize profit?

LET X ACRES OF CROP A BEPLANTED..................X<=15 ACRES AS LIMITED

THEN CROP B IS PLANTED IN 20-X ACRES

COST OF SEED FOR CROP A = 120X......COST OF SEEDFOR CROP B = 200(20-X)=4000-200X

LABOR COST FOR CROP A = 15*5.6X=84X......LABORCOST FOR CROP B = 10*5(20-X)=1000-50X

EXPECTED INCOME FROM CROP A = 600X....EXPECTED INCOME FROM CROP B =520(20-X)=10400-520X

TOTAL PROFIT=600X+10400-520X-[120X+4000-200X+84X+1000-50X]

TOTAL PROFIT=80X+10400-46X-5000=34X+5400

THAT IS PROFIT INCREASESWITH X .SO WE SHOULD HAVE AS HIGH X ASPOSSIBLE.

BUTX<=15

SO 15 ACRES SHALL BE USEDFOR CROP A................C IS THEANSWER

A. 5 acres

B. 20 acres

C. 15 acres......................IS THE RIGHTCHOICE

D. infeasible

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