4. Maximize the daily output in producing x₁ chairs byProcess P₁ and x2 chairs by Process P₂ subject to3x1 + 4x2 ≤ 550 (machine hours), 5x1 + 4x2 ≤ 650(labor).5. Minimize f= 5x120x2 subject to -2x1 + 10x2≤5, 2x1 + 5x2 ≤ 10.

As per our guideline we supposed to answer only first question Daily output Z= x1+x2 subject…

Answered: 4. Maximize the daily output in…

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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Optimization Problem: Q: What is the largest possible volume of an open vox that you can built from a fixed amount of paper (say 1000 square inches), if the length of the base is 3 times the width?
5) Given P=5900-10Q, Costs that will not change due to production is $845 and Cost that depends on use of Electricity, gas, Raw materials, Labour, etc. is given by the function 2Q^3 - 4Q^2 +140Q.Find optimal output, price and maximum profit and verify using second order conditions.
The following is a L.P.P: Max Z- 5X1+7X2+ 6X3 (Hundreds of dollars $) s.t: 3X1+ 4X2 + 2X3 -0 (production capacity; hours) (warehouse capacity: hundreds of sq. ft.) (demand for 6 oz. glasses: hundreds of cases) The optimal solution to the model as follows: Basis Св 5X1 7X2 S1 6X3 0.5 -1 S2 S3 RHS X2 S1 X1 1. -0.5 10 1. -3 10 1. -1 10 7. 1.6 -1.5 5n 8.5 120 C-Z 01 -2.5 -2 What effect on the optimal solution (value of Z) ,if we change b2 from 48.2 to 57.1 ?
17. Suppose you are designing a rectangular box with a square base. The materials of which the base and the top is made is $16 per square meter. The cost of the material of which the sides of the box are made is $9 per square meter. (a) If the volume of the box is 1m³, find the dimensions of the box minimizing its cost. 7 (b) What is the largest volume of the box that can be made of $36 worth of materials? (c) If the surface area of the box needs to be 800 m², what are the dimensions that give the largest volume. possible? (d) If the volume of the box is 1m³, find the dimensions of the box minimizing its surface area. V = 1wh 1wh=1m³ | wh="36
2. The Minimum point of y= 8x+4 (x-2)²
Solve the following optimization problems

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4. Maximize the daily output in producing x₁ chairs by Process P₁ and x2 chairs by Process P₂ subject to 3x1 + 4x2 550 (machine hours), 5x1 + 4x2 ≤ 650 (labor).