A company manufactures x units of Product A and y units of Product B, on two machines, I and II. The company will realize a profit of $4/unit of Product A and a profit of $4/unit of Product B. Manufacturing 1 unit of Product A requires 6 min on Machine I and 5 min on Machine II. Manufacturing 1 unit of Product B requires 9 min on Machine I and 4 min on Machine II. There are 5 hr of time available on Machine I and 3 hr of time available on Machine II in each work shift. (a) How many units of each product should be produced in each shift to maximize the company's profit? The maximum is P = 160 v at (x, y) = ( 20,20 (b) Suppose P= cx + 4y. Find the range of values that the contribution to the profit of 1 unit of Product A, the coefficient c of x, can assume without changing the optimal solution. scs (c) Find the range of values (in hours) that the resource associated with the time constraint on Machine I can assume. s (resource) s (d) Find the shadow price for the resource associated with the time constraint on Machine I.

A company manufactures x units of Product A and y units of Product B, on two machines, I and II. The company will realize a profit of $4/unit of Product A and a profit of $4/unit of Product B. Manufacturing 1 unit of Product A requires 6 min on Machine I and 5 min on Machine II. Manufacturing 1 unit of Product B requires 9 min on Machine I and 4 min on Machine II. There are 5 hr of time available on Machine I and 3 hr of time available on Machine II in each work shift. (a) How many units of each product should be produced in each shift to maximize the company's profit? The maximum is P = 160 v at (x, y) = ( 20,20 (b) Suppose P= cx + 4y. Find the range of values that the contribution to the profit of 1 unit of Product A, the coefficient c of x, can assume without changing the optimal solution. scs (c) Find the range of values (in hours) that the resource associated with the time constraint on Machine I can assume. s (resource) s (d) Find the shadow price for the resource associated with the time constraint on Machine I.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 27EQ

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