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Solve the following linear programs by graphical method. Use extra sheets of paper if necessary.
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- If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.Use the information below to answer question 2x + 3y + 3z = 2 4x – 3y – 6z = 2 10x – 6y + 3z = 0 1. Given values – 144, -192, and 96 for Dx, Dy, and Dz respectively and D = 144. Then the solution to the system for x, y and z are: A. -1, -1.33, and 0.67 B. -0.47, -0.63 and 0,30 C. 0.5, 0.67 and-0.33 D. 0.73, 0.98 and -0.4925. Consider the following list of retail items sold in a small neighborhood gift shop.Average ProfitItem Annual Volume per ItemGreeting cards 3,870 $ 0.40T-shirts 1,550 1.25Men’s jewelry 875 4.50Novelty gifts 2,050 12.25Children’s clothes 575 6.85Chocolate cookies 7,000 0.10Earrings 1,285 3.50Other costume jewelry 1,900 15.00a. Rank the item categories in decreasing order of the annual profit. Classify eachin one of the categories as A, B, or C.b. For what reason might the store proprietor choose to sell the chocolate cookieseven though they might be her least profitable item?
- Consider the linear program max 4y_{1} + 5y_{2} s.t. - y_{1} + y_{2} <= 4 y_{1} - y_{2} <= 10 y_{1}, y_{2} >= 0 (a) Show graphically that the model is unbounded.Set up the simplex matrix used to solve the linear programming problem. Assume all variables are nonnegative. Maximize f = 8x + 9y + 3z subject to 2x + 7y + 8z ≤ 100 6x + 3y + z ≤ 160 3x + 4y + 9z ≤ 10 .What combination of x and y will yield the optimum for this problem? Maximize $10x + $4y, subject to (1) 5x + 3y ≤ 15 and (2) 3x + 6y ≤ 18 and (3) x, y ≥ 0.
- Calculate the linear programming: Min. Z = 6X1+3X2 Constraints 2X1+4X2 ≥ 16 4X1+3X2 ≥ 24 X1,X2 ≥ 0For a table manufacturing company, selling price for a table is $183.00 per Unit, Variable cost is $25.00 per Unit, rent is $3,380.00 per month and insurance is $296.00 per month. Company wants to expand its business and improve the table quality, it wants to increase the selling price for a table to $254.00 per Unit, Variable cost to $43.00 per Unit, bigger area will have rent $5,235.00 per month and insurance is $362.00 per month At what point will the company be indifferent between the current mode of operation and the new option?Don't use chatgpt, I will 5 upvotes Alan wants to bake blueberry muffins and bran muffins for the school bake sale. For a tray of blueberry muffins, Alan uses 1/3 cup of oil and 2 eggs. For a tray of bran muffins, Alan uses 1/2 cup of oil and 1 egg. Alan has 4 cups of oil and 12 eggs on hand. He sells trays of blueberry muffins for $12 each and trays of bran muffins for $9 each. Alan wants to maximize the money raised at the bake sale. Let x represent the number of blueberry muffins and y represent the number of bran muffins Alan bakes.
- Find solution using simplex method MAX Z = 6x1 + 4x2subject tox1 + x2 ≤ 5x2 ≥ 8and x1,x2 ≥ 0Find the minimum value of the function z=2x+2y subject to the following constraints. x≤17 y≤16 5x+2y≥42 3x+11y≥84May I have the linear programming graph (or model) or plot with the given following information? 3 variables and 8 contraints Objective - Zmax = 1.85R+2.1D+2.15H Constraints: 0.15R + 0.2D + 0.25H ≤ 6000 0.25R + 0.2D + 0.15H ≤ 7500 0.25R + 0.2D + 0.15H ≤ 7500 0.10R + 0.2D + 0.25H ≤ 6000 0.25R + 0.2D + 0.20H ≤ 7500 R ≥ 10000 D ≥ 3000 H ≥ 5000