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Martin is pla...

Question

Martin is planning which crops to plant on his farm for the upcoming season. He has enough seed to plant $4$ acres of wheat and $7$ acres of soybeans, but the total area of farmland he owns is only $9$ acres. He earns 90 $p e r a c r e f o r e v e r y a c r e o f w h e a t p l a n t e d a n d$ $120$ for every acre of soybeans planted, and he must pay a $10$ % tax on all money he earns from selling his crops. Calculate the maximum profit, in dollars that Martin can earn from planting wheat and soybeans this season.

A

918

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B

916

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C

914

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D

912

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Solution

The correct option is A $918$
In order to find the greatest profit, maximize the number of acres of soybeans Martin plants, since soybeans bring in more money per acre than does wheat. At most, MartIncan plant $7$ acres of soybeans.
Therefore, the most money he can make on soybeans is $7 \times 120 = 840$ .
He then has $9 - 7 = 2$ acres left on which to plant wheat.
The money he makes from this wheat is $2 \times 90 = 180$ .
The total amount Martin makes before taxes is therefore $840 + 180 = 1, 020$ .
The tax on this money equals $1020 \times 0.10 = 102$ .
Subtract the amount Martin pays in taxes to get $1, 020 - 102 = 918$ profit.
The correct answer is $918$ .

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