Login/Sign Up
Home » A fruit grower can use two types of fertilizer in his garden, brand P and brand Q. The amounts (in kg) of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in the table, Tests indicate that the garden needs at least 240 kg of phosphoric acid, at least 270 kg of potash and at most 310 kg of chlorine.If the grower wants to minimize the amount of nitrogen added to the garden, how many bags of each brand should be used? What is the minimum amount of nitrogen added in the garden?
A fruit grower can use two types of fertilizer in his garden, brand P and brand Q. The amounts (in kg) of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in the table, Tests indicate that the garden needs at least 240 kg of phosphoric acid, at least 270 kg of potash and at most 310 kg of chlorine.If the grower wants to minimize the amount of nitrogen added to the garden, how many bags of each brand should be used? What is the minimum amount of nitrogen added in the garden?
CBSE | Class 12 | Linear Programming | Maths | Miscellaneous | NCERT
A fruit grower can use two types of fertilizer in his garden, brand P and brand Q. The amounts (in kg) of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in the table, Tests indicate that the garden needs at least 240 kg of phosphoric acid, at least 270 kg of potash and at most 310 kg of chlorine.If the grower wants to minimize the amount of nitrogen added to the garden, how many bags of each brand should be used? What is the minimum amount of nitrogen added in the garden?
Kg per bag
Brand PBrand Q
Nitrogen33.5
Phosphoric acid12
Potash31.5
Chlorine1.52

Allow the organic product cultivator to utilize x packs of brand P and y sacks of brand Q individually

The issue can be defined as given beneath

    \[Limit\text{ }z\text{ }=\text{ }3x\text{ }+\text{ }3.5y\text{ }\ldots \text{ }\ldots \text{ }.\text{ }\left( I \right)\]

Subject to the requirements,

    \[x\text{ }+\text{ }2y\text{ }\ge \text{ }240\text{ }\ldots \text{ }\ldots \text{ }..\text{ }\left( ii \right)\]

    \[x\text{ }+\text{ }0.5y\text{ }\ge \text{ }90\text{ }\ldots \text{ }..\text{ }\left( iii \right)\]

    \[1.5x\text{ }+\text{ }2y\text{ }\le \text{ }310\text{ }\ldots \text{ }\ldots \text{ }..\text{ }\left( iv \right)\]

    \[x,\text{ }y\text{ }\ge \text{ }0\text{ }\ldots \text{ }\ldots \text{ }.\text{ }\left( v \right)\]

The achievable locale controlled by the arrangement of limitations is given underneath

NCERT Solutions Mathematics Class 12 Chapter 12 - 43

A (240, 0), B (140, 50) and C (20, 140) are the corner points of the achievable locale

The worth of z at these corner focuses are given beneath

Corner point

    \[z\text{ }=\text{ }3x\text{ }+\text{ }3.5y\]

 

A (140, 50)          595

B (20, 140)          550

C (40, 100)          470        Minimum

The greatest worth of z is 470 at (40, 100)

Thusly, 40 packs of brand P and 100 sacks of brand Q ought to be added to the nursery to limit the measure of nitrogen Consequently, the base measure of nitrogen added to the nursery is 470 kg.

i

More Material