A company produces two types of computers; desktops and laptops. They will make a profit of $248 on each desktop and $259 on each laptop. Each desktop computer takes 10 hours of assembly time and 2 hours of quality control time. Each laptop computer takes 6 hours of assembly time and 7 hours of quality control time. The company has a maximum of 2,800 assembly hours and 1,000 quality control hours per week. In your answer, let x be the number of desktops to produce, and let y be the number of laptops to produce. Write the linear programming problem which must be solved to determine how many of each kind of computer should be made in order to maximize profit.

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<=28001

2. Quality control time

Quality control time 2 hours and  7 hours for desktop and laptop respectively

maximum assembly hours is 1000

2x+7y<=10002

we can now solve equation 1 and 2 to get the values of x and y

10x+6y<=28001

2x+7y<=10002

multiply equation 2 by 5 we have

10x+6y<=28001

10x+14y<50003

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<=28001

10x+6(275)<=28001

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