Question

Question 12

A company manufactures 2 types of products P1 and P2. Let X1 and X2 be their respective number of units to be produced each month.

The company has a contract with one of its customers to produce a minimum of 300 units of each product per month. This information can be expressed in the LP as follows

A) Maximize X1 + X2

B) X1+X2 ≥ 600

C) X1+X2 ≥ 300

D) X1 ≥ 300, X2 ≥ 300

Answer 1

Here the company manufactures two types of products namely P1 and P2.

X1 number of units P1 to be produced each month by the company

X2 number of units P2 to be produced each month by the company.

The company has a contract to produce minimum 300 units of each product per month.

So, value of X1 should be minimum 300 in each month, which can be expressed mathematically as

X1 ≥ 300

Similarly, value of X2 should be minimum 300 in each month, as company has to produce 300 units of each of P1 and P2 per month, as per the contract with the customer. 200

Hence,

X2 ≥ 300

So, the given expression can be expressed in the LP as

X1 ≥ 300, X2 ≥ 300

Hence option D is the correct one.

Option B says X1+X2 ≥ 600, and this information does not imply that X1 will be ≥ 300 and X2 will be ≥ 300 individually.

For example, take X1=200, X2 = 450, then X1+ X2 = 650 ≥600 But here number of produced P1 is

200 which is less than 300. Hence the contract with the customer is violated.

Similarly, option C is wrong also due to the fact that if X1 +X2 ≥ 300 then it can never imply that each of X1 and X2 is more than 300. For example, X1 = 200, X2= 200, X1+ X2 = 400 ≥ 300 but both of X1 and X2 are less than 300.

If we maximize X1 + X2, it may happen that it satisfies all the conditions of the contract, but it does not guarantee to retain the conditions of the contract.

Option D is the correct one.