$(1$ point$)$

A company produces three types of pencil holders: basic, deluxe, and supreme. All types require plastic, rubber, and silver as shown below:

$\backslash$table$[[$Type$,$Plastic,Rubber,Silver$],[$Basic$,1,2,2],[$Deluxe$,2,2,4],[$Supreme$,1,2,4]]$

The company has $1000$ units of plastic, $1400$ units of rubber, and $2200$ units of silver. It makes a profit of $$7,$$$8,$ and $$4$ respectively on basic, deluxe, and supreme pencil holders. Assuming that all pencil holders which are manufactured can be sold, determine the number of each type of pencil holder the company should produce to maximize its profit.

Number of Basic pencil holders $=$

Number of Deluxe pencil holders $=$

Number of Supreme pencil holders $=$