A television manufacturing company has two factories I and I

A television manufacturing company has two factories, I and II, that manufacture color and monochrome TV sets, Each day, factory I produces 50 color and 20 monochrome Tv sets at a cost of $3,000. Each day, factory II produces 30 color and 24 monochrome TV sets at the cost of $2,700 and 1,800 monochrome TV sets. For how many days should each factory operate in order to fill the order at the least cost?....Give me the inequalities and objection function I need to find this answer.

Solution

Let factory I operates for A days and factory II for B days fo fill the order.

So, factory I will produce 50 A and II will produce 30 B color TV sets.

Factory I will produce 20 A and II will produce 24 B monochrome TV sets.

Order is 2700 color and 1800 monochrome TV sets.

So, 50 A + 30 B = 2700 and

20 A + 24 B = 1800

Solving these 2 equations, we get A = 18 and B = 60

So, factory I should operate for 18 days and II for 60 days.

Let x be the cost of color TV sets and y be the cost of monochrome TV sets.

50 x + 20 y = 3000

30 x + 24 y = 2700

Solving these 2 equations, we get x = 30 and y = 75

Objective function is

Z = 2700 x + 1800 y

So, Z = ( 2700 * 30) + (1800 * 75)

= 81000 + 135000

= 216000

So, factory I should operate for 18 days and II for 60 days in order to fill the order at the least cost that is $216,000.