Question

A diet management system produces two types of foods A and B. Food A contains (5,15,1,2) mg. per ounce of cholesterol, calcium, iron and vitamin C respectively and Food B contains (5,15,1,2) mg. per ounce of the same nutrients in order respectively
A nutritionist wishes to minimize the cholesterol content while satisfying the minimum daily requirements (300,13,40) for calcium, iron and vitamin C respectively.

Assume that the number of ounces of the foods used is given by x,y respectively and construct the following:

The function to be minimized is:?

The restriction imposed by vitamin C need is: ? >= ?.

The restriction imposed by calcium need is: ? >= ?.

The restriction imposed by iron need is: ? >= ?.

Answer 1

Is there a typo, both foods have the same nutrition content, so there is no minimization to be done.

Ch(x,y)=5x+5y
C(x,y)=15x+15y≥300
Ca(x,y)=x+y≥13
Fe(x,y)=2x+2y≥40