Please solve questions 4, 5, and 6.

4. Two models of a product - Regular (X) and Deluxe (Y) - are produced by a company. A linear programming model is used to determine the production schedule. The formulation is as follows: Maximizeprofit50X+60YSubjectto:4X+10Y800X+Y1204X+5Y500allvariables0(laborhoursconstraint)(demandconstraint)(rawmaterialconstraint) How many units of the labor hours must be used to produce X=50 units of Regular product and Y=20 units of the Deluxe product? (5 Points) 5. The following simplex tableau give a basic feasible solution for a linear programming problem: where x,y and z are the decision variables. Find the values of these decision variables from the above tableau. (5 Points) 6. Consider a maximization linear programming problem whose initial simplex tableau is as follows: where P is the objective function value; x,y and z are the decision variables; and u,v and w are the slack variables. What will be the entering and the leaving variables? Give reasons for your answer. (6 Points)