B. Indicate how much slack resource is available at the optimalsolution point. The Xecko Tool Company is considering bidding on a job for two airplane wing parts. Each wing part must beprocessed through three manufacturing stages; stamping, drilling, and finishing for which the company haslimited available hours. The linear programming model to determine how many of part 1 (x1) and part 2 (x2)the company should produce in order to maximize its profit is as follows:MaximizeZ = $650x, + 910x2Subject to 4x, + 7.5x2 < 105 (stamping, hr.)6.2x, + 4.9x2 < 90 (drilling, hr.)9.1x, + 4.1x2 < 110 (finishing, hr.)X1, X2 20

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Answered: B. Indicate how much slack resource is…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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An Investec analyst is looking to invest R180,000 in hopes of getting the highest return possible. There are four investment options available: bonds, mutual funds, stocks, or a savings account yielding interest. The bonds give a 4% annual return, mutual funds give an 9% return, stocks give a 12% return, and the savings account gives a 3% return with all investments being subject to risk. To control for risk, the following constraints are put into place: a) No more than 12% of the total investment can be put into stocks. b) At most 30% must be invested in mutual funds and/or the savings account. c) The amount put in the bonds must be no more than the amount put into the other investments combined. d) The ratio of money invested in mutual funds to the amount invested in stocks and the savings account should be at least 2 to 1. e) All the R180,000 must be invested and no shorting is allowed. Formulate a linear programming model for this problem to get the highest return (i.e., Define…
How much should the price of product 2 be increasedto make it profitable to produce? How much of product 2 shouldbe produced in the new optimal plan?
How can we interpret non-basic slack variables within an optimal solution? Select one or more: as the amount of uninvested money cannot be interpreted as possible increase in risk as exceeding the minimum requirement to invest in gold as the annual return on the total money invested as the difference between invested money in silver and in platinum
4. A manufacturer must decide how many chairs and tables to produce in a given week. It takes 2 hours to construct a chair and 3 hours to construct a table. The finishing process requires 2 hours for each chair and 2 hours for each table. There are 36 work hours available for construction and 28 work hours available for finishing. If the profit is $15 per chair and $25 per table, how many of each should be produced to maximize profit? Define your variables. HO 8 Find the Profit or Objective Function. Construction Find the Constraint equations. Do negatives make sense? 61 y Pt d for chairs for tables ho 21139036 X20 10 12 14 1618002 2 PCXIT ISXH59 The vertices of the feasible region. y 20 finish 2x+2y ≤28 Y= y=-2 3X+12
If an optimal value exists for an objective function, it exists at one of the vertices of the feasible region. Explain how to find the vertices.
Solve the following LP Maximize $4x + $5y Subject to 2x + 3y ≤ 20 (labor, in hours) 6x + 6y ≤ 36 (materials, in pounds) 4x + 4y ≤ 40 (storage, in square feet) x, y ≥ 0 a) Write the original optimal solution and objective function value. b) What is the optimal solution and objective function value if you acquire 2 additional pounds of material? c) What is the optimal solution and objective function value if you acquire 1.5 additional hours of labor? d) What is the optimal solution and objective function value if you give up 1 hour of labor and get 1.5 pounds of material? e) What is the optimal solution and objective function value if you introduce a new product that has a profit contribution of $2? Each unit of this product will use 1 hour of labor, 1 pound of material, and 2 square feet of storage space.
5. A small business enterprise makes dresses and trousers. To make a dress, it requires ½ hour of cutting and 20 minutes of stitching. To make a trouser, it requires 15 minutes of cutting and hour of stitching. The profit on a dress is N$40 and on a pair of trousers N$50. The business operates for a maximum of 8 hours per day Determine how many dresses and trousers should be made to maximize profit and what the maximum profit is. O A The maximum profit is N$800, 10 dresses and 8 trousers OB The maximum profit is N$850, 12 dresses and 6 trousers OC The maximum profit is N$860, 12 dresses and 6 trousers OD The maximum profit is N$880, 12 dresses and 8 trousers

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B. Indicate how much slack resource is available at the optimal solution point.