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# A Dietician Wishes to Mix Two Kinds ·Of Food X· and Y in Such a Way that The Mixture Contains at Least 10 Units of Vitamin A, 12 Units of Vitamin B Arid 8 Units of Vitamin C. the Vitamin Contents of One Kg Food is Given Below - ISC (Science) Class 12 - Mathematics

ConceptGraphical Method of Solving Linear Programming Problems

#### Question

A dietician wishes to mix two kinds ·of food X· and Y in such a way that the  mixture contains at least 10 units of vitamin A, 12 units of vitamin B arid 8 units of vitamin C. The vitamin contents of one kg food is given below:

 Food Vitamin A Vitamin.B Vitamin C X 1 unit 2 unit 3 unit Y 2 unit 2 unit 1 unit

Orie kg of food X costs Rs 24 and one kg of food Y costs Rs 36. Using Linear Programming, find the least cost of the total mixture. which will contain the required vitamins.

#### Solution

Let one type of food be x and another type be y

 Food Vitamin A Vitamin B Vitamin C X 1 units 2 units 3 units Y 2 units 2 units 1 units

∴ According to the given condition

Minimize z = 24x + 36y

Subject to

x + 2y >= 10

x + 2y >= 12 or x + y >= 6

x + y >=  8

 X + 2y = 10 x + y = 6 3x + 1y = 8 x/10 + y/5 = 1 x + y = 6 x/(8/3) + y/8 = 1

 Corner points Objective functionz= 24x + 36y A(10,0) z= 24xx 10 + 36 xx 0 = 240 B(2,4) z = 24 xx 2 + 36 xx 4 = 192 C(1,5) z = 24 xx 1 + 36 xx 5 = 204 D(0,8) z = 0 xx 24 + 36 xx 8 = 288

Minimum value of z is 192 at B (2, 4)

Is there an error in this question or solution?

#### APPEARS IN

2014-2015 (March) (with solutions)
Question 13.2 | 5.00 marks
Solution A Dietician Wishes to Mix Two Kinds ·Of Food X· and Y in Such a Way that The Mixture Contains at Least 10 Units of Vitamin A, 12 Units of Vitamin B Arid 8 Units of Vitamin C. the Vitamin Contents of One Kg Food is Given Below Concept: Graphical Method of Solving Linear Programming Problems.
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