A television set manufacturing firm has to decide on the mix of color and black-and-white TVs to be produced. A market research indicates that, at most, 2000 units and 4000 units of color and black-and-white TVs can be sold per month. The maximum number of man-hours available is 60,000 per month. A color TV requires 20 man-hours and a black-and-white TV requires 15 man-hours to manufacture. The unit profits of the color and black-and-white TVs are $60 and $30, respectively. It is desired to find the number of units of each TV type that the firm must produce in order to maximize its profit. Formulate the problem as a linear program.

Objective Function,  

Subject to the Constraints

Step-by-step explanation:

Let the number of black t.v. produced =b

Let the number of colored t.v. produced =c

at most, 2000 units of color t.v. can be sold i.e.

at most 4000 units of black-and-white TVs can be sold i.e.

Total man hours per product = Number of Units X Man Hour Per Unit

A color TV requires 20 man-hours  = 20c

A black-and-white TV requires 15 man-hours =15b

Since Maximum number of man Hours is 60000 hours

The unit profits of the color TV is $60, therefore total profit =60c

The unit profits of the black-and-white TVs $30, respectively, therefore total profit =30b

Since we are to maximize profit, the Objective Function,

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

found it xd it ok yt