Question

A diet to contain at least 2400 units of vitamins, 1800 units of minerals, and 1200 calories two foods , Food A and Food B are to be purchased. Each unit of Food A provides 50 units of vitamins, 30 units of minerals and 10 calories. Each unit of food B provides 20 units of vitamins, 20 units of minerals and 40 calories. If Food A costs $2 per unit and Food B costs $1 per unit, how many units of each food should be purchased to keep costs at a minimum?

Answer 1

30 units of Food A and 45 units of Food B are to be purchased to keep costs at the minimum $105.

Step-by-step explanation:

X = Amount of food A

Y = Amount of food B

Z= 2X+Y..... minimum cost equation

50X + 20Y > 2400 .................Vitamins .......(1)

30X + 20Y > 1800 ...................Minerals.......(2)

10X + 40Y > 1200 .................Calories ..........(3)

X > 0

y > 0

X=30 and Y = 45

Z= 2(30) + 45 = $105