Page 75 - Mathematics_Form_3

Linear programming

Example 3.6

A dietitian prescribes a special diet for patients containing the following number
of units of vitamins A and B per kg of two food types, F and F . Food F contains
1
1
2
20 units of vitamin A and 7 units of vitamin B per kg, while the food F contains
2
FOR ONLINE READING ONLY
15 units of vitamin A and 14 units of vitamin B per kg. If the minimum daily
intake required is 120 units of vitamin A and 70 units of vitamin B per kg, what
is the least total mass of food a patient must have to get a sufficient amount of
the vitamins?
Solution
Make a summary of the given information in a tabular form as shown in the
following table.

Nutrients
Food Vitamin A Vitamin B
F 1 20 7
F 2 15 14
Minimum daily 120 70
requirement
Let x be the number of kg of food type F , and
1
y be the number of kg of food type F .
2
Since the requirement is to find the least total mass of food, then this is a
minimization problem.
y
x
Thus, the objective function is to minimize (, )f xy =+ .
³
Subject to: 20x 7x x ≥ 0, y ≥ 0 120 ⇒ 4x 2y + 3y + ³ 10 24
15y +
³
Mathematics for Secondary Schools Determine where the lines 4x + 4x + 3y = 3y = 0 24 and x + 6 2y = 10 intercept the
⇒ x
14y +
³
70
coordinate axes as shown in the following tables.
The x and y-intercepts for
24
x
y

The x and y-intercepts for
x + 2y = 8 10 0
x 0 10
y 5 0

68 Student\s Book Form Three

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