Question

A company produces two different products. one of them needs 1/4 of an hour of assembly work per unit, 1/8 of an hour in quality control work and rs1.2 in raw materials. the other product requires 1/3 of an hour of assembly work per unit, 1/3 of an hour in quality control work and rs 0.9 in raw materials. given the current availability of staff in the company, each day there is at most a total of 90 hours available for assembly and 80 hours for quality control. the first product described has a market value (sale price) of rs 9 per unit and the second product described has a market value (sale price) of rs 8 per unit. in addition, the maximum amount of daily sales for the first product is estimated to be 200 units, without there being a maximum limit of daily sales for the second product. formulate and solve graphically the lpp and find the maximum profit.

Answer 1

watch the screen shot

Answer 2

200 units of Product I and 120 units of Product II

Maximum profit of Rs. 2412

Step-by-step explanation:

Let number of units of Product I be x and Product II be y.

CP of x = 1.2

SP of x = 9

Profit of x = 9 - 1.2 = 7.8

CP of y = 0.9

SP of y = 8

Profit of y = 8 - 0.9 = 7.1

z = 7.8x + 7.1y ----------(1)

Assembly work:

x/4 + y/3 <= 90

3x + 4y <= 1080 -----(2)

QC work:

x/8 + y /3 <= 80

3x + 8y <=  1920 -----(3)

Maximum sale of X is 200 units.

Please refer to the graph for solving the maximum profit.

Solution: x = 200 and y = 120 for a maximum profit of Rs. 2412.

200 units of Product I and 120 units of Product II is the answer.