Formulate but do not solve the following exercise as a linear programming problem.

A company manufactures $x$ units of product $A,y$ units of product $B,$ and $z$ units of product $C.$ Each product is processed in three departments: I, II$,$ and III. The total available labor$-$hours per week for

departments I, II$,$ and III is $940,1960,$ and $830,$ respectively. The time requirements $($in hours per unit$)$ and profit per unit for each product are given in the table below. How many units of each product should

the company produce in order to maximize its profit, $P?$

$x0$

$y0$

$z0$