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Question 1202045: 1 company menufactures two products, A and B., each unit of A require 3 hours and esch unit of B roquires 5 labor hours. Dally manufacturing capacity is 150 labor hours.
(i)If x units of Product A and y units of product B art manufactured each and all labor hours ure to be used, determine the linear equation as that requires the use of 150 labor hours per day,
(ii)How many units of can be made each day if 25 of B
MANUFACTURED each day?
How many units of A can be made each week If 12 unity ofB are manufactured each day? (Assume a 5-day work week.)
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Part (i)
x = number of units of product A
y = number of units of product B
x,y are nonnegative whole numbers 0,1,2,3,4,...
Each unit of product A needs 3 hours of labor.
Making x units of them takes 3x hours of labor.
Making y units of B takes 5y hours.
The total number of labor hours would be 3x+5y.
The amount of labor hours available is 150 hours.
Therefore we arrive at the equation 3x+5y = 150 when all available labor hours are used up.
Optionally we could solve for y, but I'll let the student do this part.
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Part (ii)
Plug in y = 25 and solve for x.
3x+5y = 150
3x+5*25 = 150
3x+125 = 150
3x = 150-125
3x = 25
x = 25/3
x = 8.333 (approximate)
Round down to the nearest integer to determine that 8 units of product A can be manufactured per day when 25 units of B are made per day.
Repeat for y = 12
3x+5y = 150
3x+5*12 = 150
3x+60 = 150
3x = 150-60
3x = 90
x = 90/3
x = 30
If 12 units of B are made per day, then 30 units of product A can be made per day.
Over the 5 day work week, 5*30 = 150 units of A can be made.
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