Q. 23

# A publisher sells a hardcover edition of a book for ₹72 and a paperback edition of the same for ₹40. Costs to the publisher are ₹56 and ₹28 respectively in addition to weekly costs of ₹9600. Both types require 5 minutes of printing time although the hardcover edition requires 10 minutes of binding time and the paperback edition requires only 2 minutes. Both the printing and binding operations have 4800 minutes available each week. How many of each type of books should be produced in order to maximize the profit? Also, find the maximum profit per week.

Answer :

Let x and y be number of hardcover and paperback edition of the book.

∴According to the question,

5x + 5y , 10x + 2y

Maximize Z = (72x + 40y) – (56x + 28y + 9600)

= 16x + 12y - 9600

The feasible region determined by 5x + 5y , 10x + 2y is given by

The corner points of feasible region are A(0,0) , B(0,960) , C(360,600), D(480,0).The value of Z at corner points are

The maximum value of Z is 3360 at point (360,600).

Hence, the publisher should publish 360 hardcover edition and 600 and paperback edition of the book to earn maximum profit of Rs.3360.

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PREVIOUSA publisher sells a hardcover edition of a book for ₹72 and a paperback edition of the same for ₹40. Costs to the publisher are ₹56 and ₹28 respectively in addition to weekly costs of ₹9600. Both types require 5 minutes of printing time although the hardcover edition requires 10 minutes of binding time and the paperback edition requires only 2 minutes. Both the printing and binding operations have 4800 minutes available each week. How many of each type of books should be produced in order to maximize the profit? Also, find the maximum profit per week.NEXTA gardener has a supply of fertilizers of the type 1 which consist of 10% nitrogen and 6% phosphoric acid, and of the type II which consist of 5% nitrogen and 10% phosphoric acid. After testing the soil condition, he finds that he needs at least 14kg of nitrogen and 14 kg of phosphoric acid for his crop. If the type - I fertilizer costs 60 paise per kg and the type - II fertilizer costs 40 paise per kg, determine how many kilograms of each type of fertilizer should be used so that the nutrient requirement are met at a minimum cost. What is the minimum cost?

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