$A$ fruit grower can use two types of fertilizer in his garden,brand $P$ and brand $Q$. The amounts (in $kg$) of nitrogen,phosphoric acid,potash,and chlorine in a bag of each brand are given in the table. Tests indicate that the garden needs at least $240 \, kg$ of phosphoric acid,at least $270 \, kg$ of potash,and at most $310 \, kg$ of chlorine.
If the grower wants to maximize the amount of nitrogen added to the garden,how many bags of each brand should be added? What is the maximum amount of nitrogen added?
Brand $P$ ($kg$ per bag) Brand $Q$ ($kg$ per bag) Nitrogen $3$ $3.5$ Phosphoric acid $1$ $2$ Potash $3$ $1.5$ Chlorine $1.5$ $2$
If the grower wants to maximize the amount of nitrogen added to the garden,how many bags of each brand should be added? What is the maximum amount of nitrogen added?
| Brand $P$ ($kg$ per bag) | Brand $Q$ ($kg$ per bag) | |
| Nitrogen | $3$ | $3.5$ |
| Phosphoric acid | $1$ | $2$ |
| Potash | $3$ | $1.5$ |
| Chlorine | $1.5$ | $2$ |
- A$140$ bags of $P$ and $50$ bags of $Q$; Maximum nitrogen = $595 \, kg$
- B$50$ bags of $P$ and $140$ bags of $Q$; Maximum nitrogen = $640 \, kg$
- C$100$ bags of $P$ and $40$ bags of $Q$; Maximum nitrogen = $440 \, kg$
- D$20$ bags of $P$ and $140$ bags of $Q$; Maximum nitrogen = $550 \, kg$
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