A merchant has 9000 square feet of floor space for storing units of products I and II. To gain the advantage of a good price he must purchase his stock now. A unit of product I costs $6 and requires 2 square feet of space, while a unit of product II costs $3 and requires 3 square feet of space. The merchant must stock at least 500 units of product 1. He expects to make a profit of $1 from each unit of product I he stocks and $4 from each unit of product II. He is instructed to stock no more than 5000 total units of the products. The amount of product 1 that he stocks should be no more than half the amount of product 2 that he stocks. He has $18,000 available for purchasing stock, and wants to know how many units of each product to buy to maximize profit. Create the LP model for this problem.

A merchant has 9000 square feet of floor space for storing units of products I and II. To gain the advantage of a good price he must purchase his stock now. A unit of product I costs $6 and requires 2 square feet of space, while a unit of product II costs $3 and requires 3 square feet of space. The merchant must stock at least 500 units of product 1. He expects to make a profit of $1 from each unit of product I he stocks and $4 from each unit of product II. He is instructed to stock no more than 5000 total units of the products. The amount of product 1 that he stocks should be no more than half the amount of product 2 that he stocks. He has $18,000 available for purchasing stock, and wants to know how many units of each product to buy to maximize profit. Create the LP model for this problem.

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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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A merchant has 9000 square feet of floor space for storing units of products I and II. To gain
the advantage of a good price he must purchase his stock now. A unit of product I costs $6
and requires 2 square feet of space, while a unit of product II costs $3 and requires 3 square
feet of space. The merchant must stock at least 500 units of product 1. He expects to make a
profit of $1 from each unit of product I he stocks and $4 from each unit of product II. He is
instructed to stock no more than 5000 total units of the products. The amount of product 1
that he stocks should be no more than half the amount of product 2 that he stocks. He has
$18,000 available for purchasing stock, and wants to know how many units of each product
to buy to maximize profit. Create the LP model for this problem.

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kindly answer items (d) and (e)