A company sells two different products A and B. The two products are produced in a common production process and are sold in two different markets. The production process has a total capacity of 45000 man-hours. It takes 5 hours to produce a unit of A and 3 hours to produce a unit of B. The market has been surveyed and company officials feel that the maximum number of units of A that can be sold is 7000 and that of B is 10,000. If the profit is Rs 60 per unit for the product A and Rs 40 per unit for the product B, how many units of each product should be sold to maximize profit? Formulate the problem as LPP.

Asked by Sakshi | 1 year ago | 80

Let x units of product A and y units of product B be produced.

Then,

Since, it takes 5 hours to produce a unit of A and 3 hours to produce a unit of B.

Therefore, it will take 5x hours to produce x units of A and 3y hours to produce y units of B.

As, the total capacity is of 45000 man hours.

⇒5x+3y≤45000

Also,

The maximum number of units of A that can be sold is 7000 and that of B is 10,000 and number of units cannot be negative.

Thus, 0≤x≤7000

Now,

Total profit = 60x+40y

Here, we need to maximize profit

Thus, the objective function will be maximize Z=60x + 40y

Hence, the required LPP is as follows:

Maximize Z = 60x + 40y

subject to

5x+3y≤45000

x≤7000y≤10000x, y≥0

Answered by Aaryan | 1 year agoMinimize Z = 2x + 4y

Subject to

x+y≥8

x+4y≥12

x≥3, y≥2

Maximize Z = 7x + 10y

Subject to

x+y≤30000

y≤12000

x≥6000

x≥y

x, y≥0

Maximize Z = 10x + 6y

Subject to

3x+y≤122x+5y≤34 x, y≥0

Maximize Z = 15x + 10y

Subject to

3x+2y≤802x+3y≤70 x, y≥0