A diet is to contain at least 640 units of vitamins, 480 units of minerals, and

Question

A diet is to contain at least 640 units of vitamins, 480 units of minerals, and 800 calories. Two foods, Food A and Food B are to be purchased. Each unit of Food A provides 10 units of vitamins, 10 units of minerals, and 10 calories. Each unit of Food B provides 20 units of vitamins, 10 units of minerals, and 40 calories. If Food A costs $10 per unit and Food B cost $6 per unit, how many units of each food should be purchased to keep costs at a minimum? Let a be the number of units of Food A and y be the number of units of Food which should be bought What is the objective function? Enter your answer as an expression such as ax+ by rather than an equation. What is the equation for the constraint due to the number of units of vitamins which are necessary? Use an equal signrather than an inequality. What is the equation for the constraint due to the number of units of minerals which are necessary? Use an equal sign . rather than an inequality What is the equation for the constraint due to the number of units of calories which are necessary? Use an equal sign rather than an inequality

Explanation / Answer

Let x be the number of units of Food A and y be the number of units of Food B

a) Objective Function: minimum cost satisfying all requirements

Cost Function Z = (units of Food A) * (cost of unit A) + (units of Food B) * (cost of unit B)

=> 10x + 6y

b)

Vitamin constraint minimum = 640

(vitamin units in Food A) * (units of Food A) + (vitamin units in Food B) * (units of Food B) = 640

10x + 20y = 640

x + 2y = 64

c)

Mineral onstraint minimum = 480

(mineral units in Food A) * (mineral of Food A) + (mineral units in Food B) * (mineral of Food B) = 480

10x + 10y = 480

x + y = 48

d)

Calories onstraint minimum = 800

(calories units in Food A) * (calories of Food A) + (calories units in Food B) * (calories of Food B) = 800

10x + 40y = 800

x + 4y = 80

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.