Solve the linear programming problem by the simplex method. Minimize x+6y subject to the constraints shown on the right. 2x+ 5y 30 3x + 5y 55 8x + 3y 107 9x + 7y 42 ,x 0, y 0 The minimum value of x + 6y is , which is attained for x= and y=

An appliance store sells three brands of TV sets, brands A, B, and C. The profit per set is $40 for brand A, $50 for brand B, and $80 for brand C. The total warehouse space allotted to all brands is sufficient for 700 sets, and the inventory is delivered only once per month. At least 125 customers per month will demand brand A, at least 100 will demand brand B, and at least 175 will demand either brand B or brand C. How can the appliance store satisfy all of these constraints and earn maximum profit? The appliance store will maximize its profits by selling nothing brand A televisions, nothing brand B televisions, and nothing brand C televisions.