We have the following Linear-Programming problem:Obj: maximize profit = $4X, + $8X2Constraints: C : 2X1 + X2 40,C2: X1 +3X2 S 30.X1, X2 20Perform a sensitivity analysis on the resource constrained in C. Determine the shadow price for the resource.

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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…
Suppose that the consumer has available income equal to Y, and the price of the goods is respectively p1 and p2. i. Derive the expressions of the quantities that maximise the utility of the consumer under the budget constraint. ii. Provide a diagram of the optimal solution.
You choose how much time a day to devote to sleeping (s) and fun (f). Suppose you get utility, which you seek to maximise. However, you face two major restrictions: there are only 24 hours in a day, and you read somewhere that it is essential to get at least 3.50 hours of sleep every day. In the case where both inequality constraints hold with strict equality, what is the value of the multiplier attached to the second constraint? (Round to two decimal places.) Your Answer: Answer
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
The supplies, demands, and transportation costs per unit are shown on the network. (a)Develop a linear programming model for this problem; be sure to define the variables in your model. Let x11 = amount shipped from Jefferson City to Des Moines x12 = amount shipped from Jefferson City to Kansas City x13 = amount shipped from Jefferson City to St. Louis x21 = amount shipped from Omaha to Des Moines x22 = amount shipped from Omaha to Kansas City x23 = amount shipped from Omaha to St. Louis Min ???????? s.t. From Jefferson City ?????? From Omaha ??????? To Des Moines ??????? To Kansas City ???????? To St. Louis ???????????? x11, x12, x13, x21, x22, x23 ≥ 0 (b)Solve the linear program to determine the optimal solution. Amount Cost Jefferson City–Des Moines Jefferson City–Kansas City Jefferson City–St. Louis Omaha–Des Moines Omaha–Kansas City Omaha–St. Louis Total
1a and 2a please written out
QUESTION 15 Calculate the minimum value of 8x + 6y subject to the following constraints: |x + y 2 24 x + 2y 2 29 2x + y 2 28 x 20 y 2 0
Need only a handwritten solution only (not a typed one).
The contribution to profits and overhead per 100 feet of pipe is $34 for type 1 and $40 for type 2.- Formulate a linear programming model to determine how much of each type of pipe should be produced to maximize contribution to profits and to overhead, assuming that everything produced can be sold.- Find the optimal solution algebraically for the Moldex Company problem. What is the Z value when the decision variables have optimal values?

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We have the following Linear-Programming problem: Obj: maximize profit = $4X, + $8.X2 %3D Constraints: C : 2X1 + X2 S 40, C2 : X1 +3X2 S 30, X1,X2 20 Perform a sensitivity analysis on the resource constrained in C. Determine the shadow price for the resource.