Respuesta :
Answer:
248x+259y>=P (objective function)
constraints
10x+6y<=2800------1
2x+7y<=1000-------2
To maximize profit(P>=$79,905)
the company needs to produce 35 desktop computers and 275 laptops computers
Step-by-step explanation:
let x be the number of desktops to produce, and
let y be the number of laptops to produce.
let the profit be p
maximize P (objective function)
248x+259y>=P
The products are subject to the constraints (that is, the restrictions)
1. Assembly hours
assembly time 10 hours and 6 hours for desktop and laptop respectively
maximum assembly hours is 2800
10x+6y<=2800------1
2. Quality control time
Quality control time 2 hours and 7 hours for desktop and laptop respectively
maximum assembly hours is 1000
2x+7y<=1000-------2
we can now solve equation 1 and 2 to get the values of x and y
10x+6y<=2800------1
2x+7y<=1000-------2
multiply equation 2 by 5 we have
10x+6y<=2800------1
10x+14y<5000-----3
subtract equation 3 from 1 we have
0x-8y<=-2200
8y<=2200
divide both sides by 8
y<=275
substitute y=275 in equation 1 we have
10x+6y<=2800------1
10x+6(275)<=2800------1
10x+1650<=2800
10x<=2800-1650
10x<=350
divide both sides by 10 we have
x<=35
we proceed by substituting x=35 and y=275 in the objective function we have
248x+259y>=P
248(35)+259(275)>=P
8680+71225>=P
P>=$79,905