A cottage industry manufactures pedestal lamps and wooden shades. Both the products require machine time as well as craftsman time in the making. The number of hour(s) required for producing 1 unit of each and the corresponding profit is given in the following table :

Iteam  Machine time Craftsman time Profit (in rupees)
Pedestal lamp 1.5 hours 3 hours 30
Wooden shades 3 hours 1 hour  20

In a day, the factory has availability of not more than 42 hours of machine time and 24 hours of craftsman time.

Assuming that all items manufactured are sold, how should the manufacturer schedule his daily production in order to maximise the profit ? Formulate it as an LPP and solve it graphically.

 

 

Answers (1)

Let number of pedestal lamps =x

Number of wooden shades =y

Maximize Profit:   P=30x+20y

\\$According to the question :$ \\\ 1.5 x+3 y \leq 42$ $ \\\\ 3 x+y \leq 24 \\\\ $ $x \geq 0, y \geq 0$

Check profit at Corner points 

At O(0,0)  => P = 0 + 0 = 0

At A(0,14)  => P = 0 + 20x14 = Rs 280

At B(4,12)  => P = 30x4 + 20x12 = Rs 360 (Max)

At A(8,0)  => P = 30x8 + 20x0 = Rs 240

Maximum profit = Rs 360 at (number of pedestal lamps) x = 4 and (Number of wooden shades ) y = 12.

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