Test III 157 (The Last One!!)
Place your name in the upper right hand corner. Place your answers in the blanks
at the left. If you are hoping for partial marks you should show your work on a
separate sheet. 
_________________1) Find the maximum and minimum of z = 2x ! 3y
such that, x + y ! 10 , 2x + y ! 20 , and x, y ! 0 Also give the
_________________ points where the maximum and minimum occur.
__________________ 2) Solve for x and y.
x ! 2y = a
x ! y = b
__________________ 3) Solve for x and y.
1
1
x + y = 1
2
4
1
1
x ! y = 1
3
5
__________________ 4) Solve for x,y and z.
3x + y ! 2z = 2
x ! 2y + z = 2
4x ! y ! z = 4
" 0 a%
! b 0$
For the following problems let A = $
and B = #
.
'
# !a 0 &
" 0 b &%
____________ ____________5) Compute, AB and BA.
____________ ____________6) Compute, A-B and B-A.
_________________________7) Orange juice, a bagel, and a coffee from Andy’s Koffee
Kart costs a total of 4$. Kelly raises the prices such that the price of orange juice will
increase by 50% and the price of a bagel will increase by 20%. After this increase the
same purchase will cost 5.00$ and orange juice will cost twice as much as coffee. Find
the original prices.
____________ 10) Solve for x,y and z in terms of a, b, and c.
x
! z = a
x ! y
= b
x ! y + z = c
a, b, and c are just some numbers.
12) Decompose the following into its partial fractions
x2 ! x ! 6
=
(x ! 1)(x 2 ! 4)
13) Decompose the following into its partial fractions
x !1
=
x(x + 2)2
14) Decompose the following into its partial fractions
x2 + x ! 2
=
(x 2 + 1)2