A manufacture of laptop computers has four models, two with color lcd (liquid crystal display) screens (the spot model and the superba model) and two model with black and white lcd screens ( the standard model and the excel model). each model required assembly and test time and the requirements are shown in the table 2, together with the amount of time available for assembly and testing next month. LCD.

the lcd screens are purchased from and outside supplier and, because of an earthquake on japan (where the lcd screens are produced), they are in short supply. the outside supplier indicates that not more than 900 LCD screens in total could be supplied in the next month, and of these, not more than 500 could be color LCD.

it is possible for the manufacturer to make available additional hours of test time by adding a third shift at the manufacturing facility and paying overtime wages. up to 500 additional hours are available using this approach, but the premium cost is $10 per hour over that for regular time. the manufacturer can sell all the laptops of any model that can be produced. assume that the manufacturer is interested in maximizing the contribution from laptop computers (less any overtime . formulate this problem as a linear programming problem.

s standard model    excel model    sport model superba model    total available

assembly time    8    10 12 15 10,000

test time(HRS) 2    3 4    6 2,500

profit contribution    $120    $180    $240    $300

Find the solution of the initial value problem y′′+12y′+32y=0, y(0)=12 and y′(0)=−84.

FIND THE CENTROID:

a. of the region enclosed between the curves y=x^1/2 , y=1, y=2 and the y-axis.

b. of the 1st quadrant area bounded by the curve y=4-x²

c. of the region bounded by the curve y=x³ and x=y²

To appreciate how viscous drag are being computed if we have the velocity field, let us consider the following velocity field for a flow of Newtonian viscous fluid u = x + 2y v = x 2 + y w = 0 (4.158) The fluid has viscosity of 10−2 kgm−1 s −1 (a) Determine the viscous stresses on the reference fluid element.(b) Determine the viscous stress vector acting on a surface aligned at an angle of 45 degrees (counterclockwise) from the x−axis.(c) Determine the viscous force acting on the same surface if surface spans from x = 2 to x = 5 and its length in the z-direction being 2 m.

Write the proof of the dual Pappus theorem.

Find the general solution of the differential equation y′′+36y=13sec^2(6t), 0<t<π/12.

Consider these 2 functions (all with domain and codomain (Z/pZ) for some big prime p): h(x) = 1492831*x and h(x) = x³ . Why are these bad cryptographic hash functions? Give different reasons for the two.

Brad and Sam take a 30-year mortgage for a house that costs $103570. Assume the following: The annual interest rate on the mortgage is 4.3%. The bank requires a minimum down payment of 20% of the cost of the house. The annual property tax is 1.6% of the cost of the house. The annual homeowner's insurance is $674. There is no PMI. If they make the minimum down payment, what will their monthly PITI be? Round your answer to the nearest dollar.

Given a quadric surface in the xyz-space with equation
ax2 + by2 + cz2 = d, where a, b, c, d are real constants, that passes through the points (1,1,−1), (1,3,3) and (−2,0,2), find a formula for the quadric surface.

1. Approximate the integral,
exp(x), from 0 to 1,
using the composite midpoint rule, composite trapezoid rule, and composite Simpson’s method. Each method
should involve exactly n =( 2^k) + 1 integrand evaluations, k = 1 : 20. On the same plot, graph the absolute error
as a function of n.

ODE: draw the phase by MATLAB ?′1=−8?1−2?2 and ?′2=2?1−4?2