graphical method & simplex method

Worksheet No. 1 Directions: Solve the following problems completely. For part 1, use the graphical method. For part 2, use simplex method (Big M Method). Part 1 1. Maximize: Z; = 10x + 20y Constraints:x + y 23 x + y 0 2. Minimize: Z; = 50x + 20y Constraints: x +y > 5 x +y = 10 x > 2 x 0 y20 Part 2 3. ChemLabs uses raw materials I and II to produce two domestic cleaning solutions, A and B. The daily availabilities of raw materials I and II are 150 and 145 units, respectively. One unit of solution A consumes 0.5 unit of raw material and 0.6 units of raw material II. One unit of solution B uses 0.5 unit of raw material I and 0.4 unit of raw material II. The profit per unit of solutions A and B are 8USD and 10USD, respectively. The daily demand for solution A lies between 30 and 50 units, and that for solution B between 40 and 200 units. Find the optimal production amounts of A and B. 4. Four foods X1, X2, X3, X4 are to be produced. x, contains 2 units of calories, no vitamins and costs P40 per unit. x2 contains no calorie, 2 units of vitamins and costs P100. Xz contains 1 unit of calorie, 1 unit of vitamins and costs P120 per unit. x4 contains 3 units of calorie, 2 units of vitamins and costs P150 per unit. The minimum calorie requirement is 15 units and the minimum vitamin requirement is 8 units. How much of each food should be produced to satisfy these requirements and to minimize the total cost