A clothier makes coats and slacks. The two resources required are wool cloth and labor. The clothier has $150$ square yards of wool and $200$ hours of labor available. Each coat requires $3$ square yards of wool and $10$ hours of labor, whereas each pair of slacks requires $5$ square yards of wool and $4$ hours of labor. The profit for a coat is $$50,$ and the profit for slacks is $$40.$ The clothier wants to determine the number of coats and pairs of slacks to make so that profit will be maximized. Formulate a linear programming model for this problem. Define $x_1$ as the number of coats, $x_2$ as the number of pairs of slacks, and $Z$ as the total profit. Which of the following model formulations is correct?