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Help me pls. This needs to be solved by the matrix method

To produce one unit of A requires 3 units of M1, 2 units of M2 and 6 units of M3. To produce one unit of B requires 3 units of M1, 2 units of M2, and 4 units of M3. To produce one unit of C requires 4 units of M3, 5 units of M1, and 7 units of M2. The manufacturer has an everyday available quantity of 71 thousand units of M1, 81 thousand units of M2 and 92 thousand units of M3.

1 Answer

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Answer:

Explanation:

Given this information, we can determine the maximum number of units of each product (A, B, and C) that can be produced with the given quantity of resources (M1, M2, and M3). To do this, we can use the formula:

Maximum number of units of product = Minimum of (available quantity of resource / resource required per unit of product)

For example, to find the maximum number of units of product A that can be produced, we take the minimum of the following three values:

(71,000 units of M1 / 3 units of M1 per unit of A) = 23,666.67 units of A

(81,000 units of M2 / 2 units of M2 per unit of A) = 40,500 units of A

(92,000 units of M3 / 6 units of M3 per unit of A) = 15,333.33 units of A

So the maximum number of units of A that can be produced is 15,333.33 units.

Similarly, we can find the maximum number of units of B and C that can be produced:

(71,000 units of M1 / 3 units of M1 per unit of B) = 23,666.67 units of B

(81,000 units of M2 / 2 units of M2 per unit of B) = 40,500 units of B

(92,000 units of M3 / 4 units of M3 per unit of B) = 23,000 units of B

So the maximum number of units of B that can be produced is 23,000 units.

(71,000 units of M1 / 5 units of M1 per unit of C) = 14,200 units of C

(81,000 units of M2 / 7 units of M2 per unit of C) = 11,571.43 units of C

(92,000 units of M3 / 4 units of M3 per unit of C) = 23,000 units of C

So the maximum number of units of C that can be produced is 11,571.43 units.

It is important to note that these calculations are based on the assumption that all resources are used fully and no resources are left over.

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