Question

UB-sweets” produces only two types of chocolate: A and B. Both the chocolates require Milk and Coco-powder only. To manufacture each unit of A and B, the following quantities are required:

Each unit of A requires 1 unit of Milk and 3 units of Coco-powder
Each unit of B requires 1 unit of Milk and 2 units of Coco-powder
UB has a total of 5 units of Milk and 12 units of Coco-powder. On each sale, UB makes a profit of

$6 per unit A sold
$5 per unit B sold.
If UB wishes to maximize its profit, how many units of A should it produce?

Answer 1

Answer:

$\huge \mathfrak \pink {A}\green{N}\orange {S}\red{W}\blue {E}\purple {R}$

Step-by-step explanation:

Let’s construct the table to represent the problem

Milk

Choco

Profit per unit

A

1

3

6

B

1

2

5

Total

5

12

Let X is total number of units produced by A

Let Y is total number of units produced by A

and Z is the total profit

how to calculate the total profit of the company

just multiply the total number of units A and B produced and Per unit profit

6 and 5 respectively

so

Profit

Max Z=6X+5Y

That means we need to maximize the profit z

The company will try to maximize the profit by producing as many as units of A and B

but the problem is Milk and Choco resources are limited

from the table,

A and B need 1 unit of Milk

But the Milk is available only 5 units

how to represent this in mathematically

X+Y<=5

And also

each unit of A, B need 3 , 2 units of choco

but total amount of choco is only 12 units

again

represent it mathematically

3X+2Y<=12

A can only integer value

and we have 2 more constraints

X>=0

Y>=0

If the company wants to make maximum profit, they should satisfy the inequalities mentioned

Hope it helps you.