1. Consider the problem below:Min (z) = -2x, - x2Subject to:X1 +x2< 52x1 + 3x2 < 12X1 < 4X1,X2 2 0Solve the given LP model by determining the optimal solution using graphical method and apply the postoptimal analysis.

Answered: Image /qna-images/answer/824006d1-c460-4bd0-983d-57fcd73e5adc.jpg

Answered: 1. Consider the problem below: Min (z)…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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A corporation manufactures candles at two locations. The cost of producing x1 units at location 1 is C1 = 0.02x1? + 3x1 + 500 and the cost of producing x2 units at location 2 is C2 = 0.05x22 + 3x2 + 325. The candles sell for $11 per unit. Find the quantity that should be produced at each location to maximize the profit P = 11(x1 + X2) – C1 – C2. X1 X2
Solve this LP max z = 3x1 + 2*2 + 2.5x3 8.t. has optimal tableau. So B = ā13 5₁ 1+ 2+ 2013 2x1 + 2x3 1, 2, 3 > 0 = 1; 1 1 0 2 and B-¹ = 15₂ 3 = <4 <6 and using B-¹ and B-¹cgy formulas the missing values in optimal tableau are C = 2.5; C = 3 ); 131 = 28 = 0 0; 1 1 2 0 11/123 and cay = 2 3 Z 21 1 0 0 0 0 1 2 Ty 81 0 Ts Ca 1 0 ā13 ā23 rhs Ž $2 1/2 1 -1/2 ₁ 0 1/2 5₂ and the optimal solution for zis z = 11 Now find the maximum amount A = 2.5 that the value of c can be increased so that the optimal BV remains optimal.
12. Suppose the cost of a product with a quantity of x is C(x) = 2x² - 6x² + 15x, and the income from selling the product x is R(x) = x² + 9x. How many products to produce for maximum profit?
Raggs, Ltd. a clothing firm, determines that in order to sell x suits, the price per suit must be p = 130-0.75x. It also determines that the total cost of producing x suits is given by C(x)=3000+ 0,5x² a) Find the total revenue, R(x). b) Find the total profit, P(x). c) How many suits must the company produce and sell in order to maximize profit? d) What is the maximum profit? e) What price per suit must be charged in order to maximize profit?
Sketch the following problem graphically: max f = x2 X2 subject to g1 = X1 – (1 – x2)³ < 0 92 = x1 2 0 Find the solution graphically. Apply the optimality conditions and monotonicity rules. Discuss. (From Kuhn & Tucker, 1951.)
Suppose that the total revenue from producing and selling q items is given by R(q) = 50g – 0.5q? - and the total cost of producing q items is given by C(q) = 4q + 10 (a) What is the profit function P(q)? (b) What is the maximum profit? (c) How many items must be produced and sold to yield the maximum profit?

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1. Consider the problem below: Min (z) = -2x-×2 Subject to: X1 + X25 5 2x1 + 3x2 S 12 X1 5 4 X1, X2 2 0 Solve the given LP model by determining the optimal solution using graphical method and apply the post optimal analysis.