Formulate a linear programming model for this problem, to determine how many containers of each product to produce tomorrow in order to maximize the profits. The company makes four types of juice using orange, grapefruit, and pineapple. The following table shows the price and cost per quart of juice $($one container of juice$)$ as well as the number of kilograms of fruits required to produce one quart of juice.

Product

Price$/$quart

Cost$/$quart

Fruit needed

Orange juice

$3$

$1$

$1$ Kg$.$

Grapefruit juice

$2$

$0\mathrm{.}5$

$2$ Kg$.$

Pineapple juice

$2\mathrm{.}5$

$1\mathrm{.}5$

$1\mathrm{.}25$ Kg$.$

All $-$in $-$ one

$4$

$2$

$0\mathrm{.}25$ Kg each