A New Office Plant$(10\%)$

As the new VP of Supply Chain for a large corporation, you have been given a nice

corner office, with large windows and a view of the river. To celebrate this good news,

your spouse has made a special gift to you: a potted specimen of Pirripirri patchiflora,

an exotic plant from Tasmania that flowers only once a year and smells vaguely like

asparagus.

To stay alive, the Pirripirri plant requires a specific combination of nutrients dissolved in

its watering solution every day. Your spouse, who is very keen on this plant's health,

has explained that its daily watering solution requires between $1800$ mg and $2200$ mg of

Nitrogen, and exactly $100$mg of Potassium.

Your spouse has been kind enough to send you the link to three products that you can

buy online, which you can dissolve in the daily watering solution for the Pirripirri:

Product #$1$ has $360$ mg of Nitrogen and $30$ mg of Potasium per gram, and costs

$1\mathrm{.}59$ cents per gram.

Product #$2$ has $380$ mg of Nitrogen and $20$ mg of Potasium per gram, and costs

$2\mathrm{.}19$ cents gram.

Product #$3$ has $310$ mg of Nitrogen and $20$ mg of Potasium per gram, and costs

$2\mathrm{.}99$ cents per gram.

You intend to spend as little as possible on these products, while meeting the nutritional

requirements of the plant.

Part $1$

You want to figure out how many grams of each product you should buy in order to

minimize the daily cost of keeping the Pirripirri alive. $($Please enter your answer in

grams, with two decimals, with no weight unit. For example, if your answer is $1\mathrm{.}2345$

grams, enter $1\mathrm{.}23$ in the space.$)$

$1\mathrm{.}1$ Grams of Product $1?$ :

$1\mathrm{.}2$ Grams of Product $2?$ :

$1\mathrm{.}3$ Grams of Product $3?$:

Part $2$: Maintenance Costs for the Plant

$2\mathrm{.}1$ What is the minimum cost, in cents per day, to keep the plant properly nourished? $($Please

enter your answer with two decimals, with no unit. For example, if your answer is $1\mathrm{.}2345$ cents,

enter $1\mathrm{.}23$ in the space.$)$

$2\mathrm{.}2$ How many mg of Nitrogen would your solution provide to the plant every day? $($Please round

your answer to integer number$)$