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?

Question

Computers and Technology

Larry Spencer

7 July, 07:43

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?

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Answers (1)

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William Rollins · Answer 1

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

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