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Algebra
Question

5) A small farmer grows two crops every year: pota...

5) A small farmer grows two crops every year: potatoes and cabbages. In order to qualify for a grant he must plant at least \( 1 \) row of potatoes, and at least \( 2 \) rows of cabbages. He has just enough seed this year to plant no more than \( 10 \) rows of potatoes. 

When he sells his crops at the local market he gets \( € 30 \) for each row of potatoes, and \( € 20 \) for each row of cabbages. 

If his land can only accommodate \( 14 \) rows of crops, help him figure out how many rows of potatoes and how many rows of cabbages he should grow in order to maximise his earnings. 

(a) Letting \( x = \) the number of rows of potatoes, and \( y = \) the number of rows of cabbages, write down the objective function for this problem. 

Answer

x > 0 , y > 0  , x + y \(\le\)14 , x \(\le\) 10 ,  Z = 30x + 20y  , solution x = 10 , y = 4

Solution
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