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System of Linear Equations

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Attached are problems involving linear equations. Thank you for your help.

1.) The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring and 2 man-hours to make one SST ring. How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $40 and on an SST ring is $35?

How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $40 and on an SST ring is $35?
a. 14 VIP and 10 SST
b. 18 VIP and 6 SST
c. 16 VIP and 8 SST
d. 12 VIP and 12 SST

2. The Acme Class Ring Company designs and sells two types of ring: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring and 2 man-hours to make one SST ring.

How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $60 and on an SST ring is $20.

a. 24 VIP and 4 SST
b. 20 VIP and 0 SST
c. 20 VIP and 4 SST
d. 24 VIP and 0 SST

3. Factories A and B sent rice to stores 1 and 2.
A sent 10 loads and B sent 22. Store 1 used 15 loads and store 2 used 17.
It cost $200 to ship from A to 1.
It cost $350 to ship from A to 2, and $300 to ship from B to 1 and
$250 from B to 2. $7750 was spent. How many loads went where?

a. 10 from A to 1
0 from, A to 2
5 from B to 1
17 from B to 2

b. 0 from A to 1
10 from, A to 2
17 from B to 1
5 from B to 2

c. 9 from A to 1
1 from, A to 2
6 from B to 1
4 from B to 2

d. 8 from A to 1
2 from, A to 2
7 from B to 1
15 from B to 2

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Solution provided by:
Gaurav Agarwal, MS
Education
  • BE, Bangalore University, India
  • MS, University of Wisconsin-Madison
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