Kim Walrath has a nutitional deficiency and is told to take

Kim Walrath has a nutitional deficiency and is told to take at least 2400 mg of iron, 2100 mg of vitamin B-1, and 1500 mg of vitamin B-2. One Maxivite pill contains 40 mg of iron, 10 mg of vitamin B-1, and 5 mg of vitamin B-2 and costs 6 cents. One Healthovite pill provides 10 mg of iron, 15 mg of vitamin B-1, and 15 mg of vitamin B-2 and costs 8 cents.

A) What combination of Maxivite and Healthvite pills will meet Kim\'s requirements at lowest cost? What is the lowest cost?

B) In your solution for part (a), does Kim receive more than the minimum amount she needs of any vitamin? If so, which vitamin is it?

C) Is there any way that Kim can avoid receiving more than the minimum she needs and still meet the other constraints and minimize the cost? Explain

Solution

Let a represents the number of maxivite pills

Let b represents the number of healthivite pills

Optimize the function

z = 6a + 8b (since the cost of maxivite pill is 6 cents and cost of healthovite pill is 8 cents)

hence the constraints are

40a + 10b >= 2400

10a + 15b >= 2100

5a + 15b >= 1500

hence we need to make a tabular starting and minimize the consists of all possible answer

the value of a comes out to be 30 and b comes out to be 120

a) Lowest cost

=> 30 * 6 + 120 * 8

=> 180 + 960

=> 1140 cents

b) the excess vitamin is vitamin-B2

Required = 1500 mg

Getting = 30 * 5 + 120 *15

=> 2040

Excesss = 840 mg