In a standard maximum linear programming problem, there are 5 decision variables used in the constraints and the system of equations in the simplex method uses a total of 9 variables. (z is not counted as a variable here.) Find the following a.) The number of constraints in the problem b.) The number of non-basic variables in the initial simplex tableau c.) The number of basic variables in the initial simplex tableau

Use Excel to solve the linear programming problem.At one of its factories, a manufacturer of televisions makes one or more of four models of HD units (without cases): a 20-in. LCD, a 42-in. LCD, a 42-in. plasma, and a 50-in. plasma. The assembly and testing time requirements for each model are shown in the table, together with the maximum amounts of time available per week for assembly and testing. In addition to these constraints, the supplier of cases indicated that it would supply no more than 290 cases per week and that of these, no more than 40 could be for the 20-in. LCD model.Use the profit for each television shown in the table to find the number of completed models of each type that should be produced to obtain the maximum profit for the week. Find the maximum profit. 20-in. LCD        sets 42-in. LCD        sets 42-in. plasma        sets 50-in. plasma        sets profit     $     20-in.LCD 42-in.LCD 42-in.Plasma 50-in.Plasma TotalAvailable Assembly  time…

Acme Block Company has orders for 80 tons of concrete blocks at three suburban locations as follows: Northwood-25 tons Westwood-45 tons Eastwood-10 tons Acme has two plants, each of which can produce 50 tons per week. Delivery cost per ton from each plant to each suburban location is as follows: Northwood Westwood Eastwood Plant 1 Plant 2 1 24 30 Which one is a correct constraint? A. X11+X12+X13 = 10 OB. X11+X12+X13 ≤ 25 OC X11+X12+X13 = 45 OD. X₁1+X12+X13 ≤ 50 30 40 ہے 40 42

A garment factory makes blouses and dresses. Each blouse gives a profit of$4, while each dress gives a profit of $5. They can sell at most 200 dresses. The number of dresses must be at least 30% of the total number of garments made. Each garment spends time(minutes) on three machines as follows:a) Show the decision variables b) Show the objective functionc) Show the constraints in standard form (i.e. suitable for using Excel’s Solver) d) Solve the linear programming problem by graphing