Practice Test 4

Calculations by S. Gramlich

21) A printing service is planning to purchase some new copy machines to meet its consumer needs.

It is considering a Model A machine which costs $3000 and prints at the rate of 35 pages per minute,

a Model B machine which costs $5000 and prints at a rate of 50 pages per minute,

and a Model C machine which costs $7000 and prints at the rate of 60 pages per minute.

The company has budgeted a total of $94,000 for the purchase of the machines and wants to be able to print a total of 57,600 pages per hour.

For these models, it wants to purchase twice as many Model A machines as Model B machines.

Assuming that the budget and printing needs are exactly met, how many of each model should be purchased?

A) 14 of Model A, 7 of Model B, 2 of Model C

B) 10 of Model A, 5 of Model B, 5 of Model C

C) 12 of Model A, 6 of Model B, 4 of Model C

D) 8 of Model A, 4 of Model B, 7 of Model C

Table:

A B C Total

costs $3000 $5000 $7000 =$94000

prints 35pg/min 50pg/min 60pg/min =57600pg/hr =960pg/min

(57600pgs/hr) x (1hr/60min)= 960pg/min

A=2B --> A-2B =0

Eqns:

3000A +5000B +7000C =94000

35A +50B +60C =960

1A -2B + 0C =0

Augmented Matrices:

A= B=

[3000 5000 7000] [94000]

[35 50 60] [960]

[1 -2 0] [0]

which can reduce using R1/1000 & R2/5:

[3 5 7] [94]

[7 10 12] [192]

[1 -2 0] [0]

inverse of A (from Excel):

[-0.666666667 0.388888889 0.277777778]

[-0.333333333 0.194444444 -0.361111111]

[0.666666667 -0.305555556 0.138888889]

invA * B = X:

[12]

[6]

[4]

and A=12, B=6, C=4

so choice C.