Set up and solve graphically the following optimization problem. [Carefully define all variables...

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Set up and solve graphically the following optimization problem. [Carefully define all variables used and explain how you obtained the objective function and the constraints, graph neatly, do any calculations required to obtain an exact solution, and report your results in the context of the situation. Acme Computer Supplies produces two home computer products: a laptop computer and a desktop computer. They both use the same CPU, and ACS can only get 120 CPUs each week. This is unfortunate as ACS has an effective sales team, and can sell as many computers as it can produce. Each desktop produces a profit of $120, and each of the desirable laptops can be sold for a profit of $180. Apart from the limitation in CPU supply, the other factors ACS has to consider are assembly time and program installation time. ACS has ten hardware technicians who assemble all the computers. They each work forty hours per week and take four hours to assemble each laptop and two hours to assemble each desktop. ACS also has eight software technicians who install the bundled software. They also work forty hours per week and take an hour to deal with each laptop. The desktops are to be sold with a very comprehensive suite of programs, so each one takes three hours installation time. (a) How many of each computer should ACS produce per week, in order to maximize its profit? (There may not be enough work to keep all the technicians busy all the time.) (b) The sales team believes that after an innovative advertising campaign focusing on the extensive software provided with the desktop computers, it will be possible to increase their price so that $200 profit is gained from each sale. In that case, what should the production schedule be?

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University of Ballarat School of Science, Information Technology & Engineering ENCOR2031 Fundamentals of Engineering (Applied Math 2) Semester 1, 2012 Assignment 3 (20 marks) 1.Set up and solve graphically the following optimization problem. [Carefully define all variables used and explain how you obtained the objective function and the constraints, graph neatly, do any calculations required to obtain an exact solution, and report your results in the context of the situation. Acme Computer Supplies produces two home computer products: a laptop computer and a desktop computer. They both use the same CPU, and ACS can only get 120 CPUs each week. This is unfortunate as ACS has an effective sales team, and can sell as many computers as it can produce. Each desktop produces a profit of $120, and each of the desirable laptops can be sold for a profit of $180. Apart from the limitation in CPU supply, the other factors ACS has to consider are assembly time and program installation time. ACS has ten hardware technicians who assemble all the computers. They each work forty hours per week and take four hours to assemble each laptop and two hours to assemble each desktop. ACS also has eight software technicians who install the bundled software. They also work forty hours per week and take an hour to deal with each laptop. The desktops are to be sold with a very comprehensive suite of programs, so each one takes three hours installation time. (a) How many of each computer should ACS produce per week, in order to maximize its profit? (There may not be enough work to keep all the technicians busy all the time.) (b) The sales team believes that after an innovative advertising campaign focusing on the extensive software provided with the desktop computers, it will be possible to increase their price so that $200 profit is gained from each sale. In that case, what should the production schedule be? [4 marks] 2.Find eigenvalues and...

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Robert · Accepted Answer

Solutions
1. Optimization problem
(a). Let ’l’ and ’d’ represent the number of laptops and desktops to
be produced per week. Let ’P’ be the profit variable to be maximized
(Objective function).
P = 180 l + 120 d
Total man-hours is 10 x 40 = 400 (hardware technicians) and 8 x 40
= 320 (software technicians).The constraint equations are
l + d ≤ 120 CPU constraint (1)
4l + 2d ≤ 400 Hard.technicians (2)
l + 3d ≤ 320 Soft.technicians (3)
l ≥ 0 (4)
d ≥ 0 (5)
The graphs plotted with the constraint equations is shown below: The
shaded area is the required area satisfying the constraints.

Set up and solve graphically the following optimization problem. [Carefully define all variables used and explain how you obtained the objective function and the constraints, graph neatly, do any...

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