Apply linear programming to this problem. A firm wants to determine how many units of each of two products $($products D and E$)$ they should produce to make the most money. The profit in the manufacture of a unit of product D is $$100$ and the profit in the manufacture of a unit of product E is $$87.$ The firm is limited by its total available labor hours and total available machine hours. The total labor hours per week are $4,000.$ Product D takes $5$ hours per unit of labor and product E takes $7$ hours per unit. The total machine hours are $5,000$ per week. Product D takes $9$ hours per unit of machine time and product E takes $3$ hours per unit. Which of the following is one of the constraints for this linear program?

$5$ D $+7$ E $=<5,000$

$9$ D $+3$ E $=>4,000$

$5$ D $+7$ E $=4,000$

$5$ D $+9$ E $=<5,000$

$9$ D $+3$ E $=<5,000$