Do the optimality test (by finding out all u₁, vj, and čij values, fill all these values in the above table) to determine if the current solution is optimal or not.
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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%.Suppose a company must service customers lying inan area of A sq mi with n warehouses. Kolesar and Blumhave shown that the average distance between a warehouseand a customer is An Assume that it costs the company $60,000 per year tomaintain a warehouse and $400,000 to build a warehouse.(Assume that a $400,000 cost is equivalent to foreverincurring a cost of $40,000 per year.) The company fills160,000 orders per year, and the shipping cost per order is$1 per mile. If the company serves an area of 100 sq mi,then how many warehouses should it have?Consider the following linear programming model: maximize Z = 3x1 + 2x2 subject to : x1 +x2 ≤ 1 x1 + x2 ≥ 2 x1,x2 ≥ 0 a) Write this model in a standard (augmented) form. (i.e. Introduce slack/surplus, artificial etc.)b) Constract the initial simplex tableau and carry on your calculations to solve this model using the simplex method. Interpret your result.
- Suppose we are solving a maximization problem andthe variable xr is about to leave the basis.a What is the coefficient of xr in the current row 0?b Show that after the current pivot is performed, thecoefficient of xr in row 0 cannot be less than zero.c Explain why a variable that has left the basis on agiven pivot cannot re-enter the basis on the next pivot.Consider the following LP problem: Min 6X+ 27Y Subject to : 2 X + 9Y => 25, and X + Y <= 75. Pick a suitable statement for this problem: a. X=37.5, Y=37.5 is the only optimal solution. b. Optimal Obj. function value is 75 c. X = 0, Y = 0 is the only optimal solution. d. Optimal Obj. function value is 0A decision problem has the following three constraints: 70X + 6Y <= 420; 24X + 3Y= 72; and 11X - Y <= 14 . The objective function is Min 17X + 38Y . The objective function value is : a. 338 b. 676 c. unbounded d. infeasible e. 0
- 25. 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?Given the region of feasible solutions with corner points of (0,3), (4,2), (6,3), and (6,6), find the corner point that would minimize the objective function z = x +10y and state the minimum. Question 3 options: 66 3 24 36A paper-recycling plant processes box board, tissuepaper, newsprint, and book paper into pulp that can be usedto produce three grades of recycled paper (grades 1, 2, and3). The prices per ton and the pulp contents of the fourinputs are shown in Table 82. Two methods, de-inking andasphalt dispersion, can be used to process the four inputsinto pulp. It costs $20 to de-ink a ton of any input. Theprocess of de-inking removes 10% of the input’s pulp,leaving 90% of the original pulp. It costs $15 to applyasphalt dispersion to a ton of material. The asphalt dispersionprocess removes 20% of the input’s pulp. At most, 3,000tons of input can be run through the asphalt dispersionprocess or the de-inking process. Grade 1 paper can only beproduced with newsprint or book paper pulp; grade 2 paper,only with book paper, tissue paper, or box board pulp; andgrade 3 paper, only with newsprint, tissue paper, or boxboard pulp. To meet its current demands, the company needs500 tons of pulp for grade 1…
- Optimal solution 4T+3C=240 2T+1C=100 →T=30, C-40 Can you please explain to me the solution and way of how he did get the exact coordinate points in the graph? I know there is a formula or way to calculate since it is hard to find out the exact point when manually plotting a graphModify the warehouse location model as suggested inModeling Issue 2. Specifically, assume that the samefour customers have the same annual shipments, butnow, there are only two possible warehouse locations,each with distances to the various customers. (Thesedistances, along with other inputs, are in the fileP07_27.xlsx.) The company can build either or bothof these warehouses. The cost to build a warehouseis $50,000. (You can assume that this cost has beenannualized. That is, the company incurs a buildingcost that is equivalent to $50,000 per year.) If onlyone warehouse is built, it will ship to all customers. However, if both warehouses are built, then the com-pany must decide which warehouse will ship to each customer. There is a traveling cost of $1 per mile.a. Develop an appropriate model to minimize totalannual cost, and then use Solver to optimize it.Is this model an NLP or an IP model (or both)?b. Use SolverTable with a single input, the traveling costper mile, to see how large…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 -0.49