Use Evolutionary Solver to solve this non-linear program. Max 3x2 + 0.4y3 1.424 s.t. 5 s x s 18 4 s y s 20 4s 2 s 18 What are the optimal values of x, yand 2? (Round your answers to nearest whole number.) Optimal values y What is the optimal value of the objective function? Use your rounded answers for x, yand 2. (Round your answer to 2 decimal places.) Optimal value I I The relationship between marketing expenditures (X) and sales (y) is given by the following formula, y= 7x 0.25x2 + 6. (Hint: Use the Nonlinear Solver tool). a. What level of marketing expenditure will maximize sales? (Round your answer to 2 decimal places.) Marketing expenditure I I b. What is the maximum sales value? (Round your answer to 2 decimal places.) Maximum sales value I I The relationship between training costs (X) and productivity (y) is given by the following formula, y = 2x + 5x2 + 33. a. Will Nonlinear Solver be guaranteed to identify the level of training that maximizes productivity? No Yes b. If training is set to 5, what will be the resulting level of productivity? (Round your answer to the nearest whole number.) Level of productivity I I A plumbing repair company has 3 employees and must choose which of 3 jobs to assign each to (each employee is assigned to exactly one job and each job must have someone assigned). Each employee can perform each job, but the cost to perform any given job can vary. The following table shows the cost for each employee to perform each job. Employee A Employee B Employee C Job 1 45 49 46 Job 2 53 52 47 Job 3 43 39 47 Solve this assignment problem in Excel to find the lowest cost solution and answer the following questions: a. Which employee is assigned to job 1? (Click to select) + b. Which employee is assigned to job 2? (Click to select) + c. Which employee is assigned to job 3? (Click to select) + d. What is the minimum cost to complete all three jobs? Minimum mostFind the optimal solution for the following problem. (Round your answers to 3 decimal places.) Maximize C = 14x + 7y subject to 8x + 12y 5 19 17x + 24y s 43 and X a 0, y 2 8. a. What is the optimal value of x? -_ b. What is the optimal value of y? -_ A manufacturer of two products (Widgets and Gadgets) makes a profit of $110 for each widget sold and $120 for each gadget sold. However, production of these products generates hazardous waste charges at the rate of 1W4 (where Wis the number of Widgets produced) and 364 (where G is the number of Gadgets produced). The manufacturer has ample supplies of all raw materials and can sell all the Widgets and Gadgets it produces. The firm has sufficient capacity to produce any realistic quantity of both products. What is the optimal quantity of each product to produce? (Round your answers to 1 decimal place.) -- What is the maximum profit the manufacturer can earn? (Round your answer to 2 decimal places.) Maximum prot I I A firm offers three different prices on its products, depending upon the quantity purchased. Since available resources are limited, the firm would like to prepare an optimal production plan to maximize profits. Product1 has the following profitability: $16 each for the first 20 units, $15 each for units 21120, and $14 for each unit over 120. Product 2's profitability is $16 each for the first 40 units, $15 each for units 4170, and $14 each for each unit over 70. The products each require 3 raw materials to produce (see table below for usages and available quantities). Product 1 usage Product 2 usage Available Quantity Raw Material (pounds per unit) (pounds per unit) (pounds) A 5 4 1,800 B 8 12 1,000 C 12 7 1,800 Use separable programming to find the optimal production plan. (Leave no cells blank be certain to enter "0" wherever required. Round the first two answers (units of Product 1 and 2) to the nearest whole number. Round the total profit answer to 2 decimal places and use unrounded unit quantities to compute it.) - units of Product 1 and - units of Product 2. :I The total prot from this plan will be Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Maximize C = 14x + 13y + 52 subject to 9x + 11y + 182 s 6 14x + 15y + 122 and x a B, y a 0, z 122 3. IV IA a. What is the optimal value of x? -_ b. What is the optimal value of y? -_