In this task you will solve maximization or minimization problems using the principles of linear programming. You will interpret the feasible region of a linear programming and apply the simplex method to solve problems. Be sure to include correct mathematical procedures and provide clear and complete explanations and interpretations. In the case that the result is decimal, you will round it to two decimal places. Use the principles of linear programming to maximize or minimize and interpret the following situation. (5 points) Maximize: z = 3x + 4y Subject to: 2x + 4y24 3x + 3y21 4x + 2y20 x, y 0 Use the principles of linear programming to maximize or minimize and interpret the following situation. (5 points) Minimize: z = 3x + 8y Subject to: x + y10 x + 2y15 y3 x, y 0 3. Sarah makes bracelets and necklaces to sell at a craft store. Each bracelet earns $ 7, takes 1 hour to assemble, and costs $ 2 for materials. Each necklace makes a profit of $ 12, takes 2 hours to assemble, and costs $ 3 for materials. Sarah has 48 hours available to put together bracelets and necklaces. If you have $ 78 available to pay for supplies, use linear programming principles to determine how many bracelets and necklaces to make to maximize your earnings. (5 points) 4. Sue runs a soccer club and must decide how many members to send to soccer camp. It costs $ 75 for each advanced player and $ 50 for each intermediate player. You cannot spend more than $ 13,250. Sue must send at least 60 more advanced than intermediate players and a minimum of 80 advanced players. Use linear programming principles to find the fraction of each type of player Sue can send to camp to maximize the fraction of players in camp. (5 points) 5. A company produces two models of calculators at two different plants. In one day, plant A can produce 140 of model 1 and 35 of model 2. In one day, plant B can produce 60 of model 1 and 90 of model 2. Suppose the company needs to produce at least 460 of model 1 and 340 for Model 2 and it costs $ 1200 per day to operate Plant A and $ 900 per day for Plant B. Use the principles of linear programming to find the minimum cost. (5 points)