Answer to Question #308532 in Linear Algebra for Lily

Question

To ensure a growing season of sufficient length, Mang Popoy has at most 16 days left to

plant corn and soybean . he can plant com at a rate of 10 hectares per day and soybean at

15 hectares per day. If he has at most 200 hectares available, how many hectares of each

type of crop can he plant?​

Answer 1

Consider the system of equations:

$\begin{cases} 10a+15b=200,\\ a,b\geq0,\\ a+b\leq16; \end{cases}$

Where $a$ is the number of days when corn is planted, $b$ – soybean.

From first equation:

$a=20-1.5b;$

Since a farmer can plant one crop per day, then $b$ must be even, otherwise $a$ will not be an integer. Let's iterate over all the values of $b\in\{0..16,\ 2|b\}$ as long as two inequalities from the system are valid:

Answer: $(a,b)=\{(8,8),(5,10),(2,12)\}$