Respuesta :
Answer:
Objective Function, [tex]Max P =60c+30b[/tex]
Subject to the Constraints
[tex]0<c\leq 2000[/tex]
[tex]0<b\leq 4000[/tex]
[tex]20c+15b\leq 60000[/tex]
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. [tex]c\leq 2000[/tex]
at most 4000 units of black-and-white TVs can be sold i.e. [tex]b\leq 4000[/tex]
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
[tex]20c+15b\leq 60000[/tex]
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, [tex]Max P =60c+30b[/tex]
For maximum profit, the equation is 60x + 30y.
Linear system
It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.
Given
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.
To find
The number of units of each TV type that the firm must produce in order to maximize its profit,
How to calculate profit?
Let x be a color TV
And y be the Black-white TV.
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.
20x + 15y = 60000
For maximum profit
The unit profits of the color and black-and-white TVs are $60 and $30, then
P(max) = 60x + 30y
Thus for maximum profit, the equation is 60x + 30y.
More about the linear system link is given below.
https://brainly.com/question/20379472
