An animal feed supply store needs to blend limestone$,$ corn and soybean meal to produce a feedstock for cattle. The nutritive content and price of the ingredients is given in the table below:

Nutritive content and price of ingredients

Ingredient

Calcium

Protein

Fiber

Unit cost

$($kg$/$kg$)$

$($kg$/$kg$)$

$($kg$/$kg$)$

$($cents$/$kg$)$

Limestone

$0\mathrm{.}38$

$0$

$0$

$10$

Corn

$0\mathrm{.}001$

$0\mathrm{.}09$

$0\mathrm{.}02$

$30\mathrm{.}5$

Soybean meal

$0\mathrm{.}002$

$0\mathrm{.}5$

$0\mathrm{.}08$

$90$

The mixture must meet the following restrictions:

$*$ Calcium: at least $0\mathrm{.}8\%$ but not more than $1\mathrm{.}2\%$

$*$ Protein: at least $22\%$

$*$ Fiber: at most $5\%$

Determine the best mixture of ingredients to meet these requirements, and then answer the questions below:

What is the total cost$/$kg of the final mixture? $($answer in cents$/$kg$)$

What is the percentage of corn in the mixture? $($answer in $\%$ to one decimal$)$

What is the total $\%$ calcium in the mixture?