To determine which ordered pair minimizes the objective function [tex]\( C = 60x + 85y \)[/tex], we will evaluate the function at each of the given pairs.
Given pairs are:
1. [tex]\( (0, 160) \)[/tex]
2. [tex]\( (55, 70) \)[/tex]
3. [tex]\( (80, 50) \)[/tex]
4. [tex]\( (170, 0) \)[/tex]
Let's calculate [tex]\( C \)[/tex] for each pair:
1. For [tex]\( (0,160) \)[/tex]:
[tex]\[
C = 60(0) + 85(160) = 0 + 13600 = 13600
\][/tex]
2. For [tex]\( (55,70) \)[/tex]:
[tex]\[
C = 60(55) + 85(70) = 3300 + 5950 = 9250
\][/tex]
3. For [tex]\( (80,50) \)[/tex]:
[tex]\[
C = 60(80) + 85(50) = 4800 + 4250 = 9050
\][/tex]
4. For [tex]\( (170,0) \)[/tex]:
[tex]\[
C = 60(170) + 85(0) = 10200 + 0 = 10200
\][/tex]
Now, let's compare these values:
- [tex]\( C(0,160) = 13600 \)[/tex]
- [tex]\( C(55,70) = 9250 \)[/tex]
- [tex]\( C(80,50) = 9050 \)[/tex]
- [tex]\( C(170,0) = 10200 \)[/tex]
The smallest value of [tex]\( C \)[/tex] is [tex]\( 9050 \)[/tex], which corresponds to the pair [tex]\( (80,50) \)[/tex].
Therefore, the ordered pair that minimizes the objective function [tex]\( C = 60x + 85y \)[/tex] is [tex]\((80,50)\)[/tex]:
[tex]\[ \boxed{(80,50)} \][/tex]
