A) Let C(x) the cost of manufacturing x refrigerators, since C is linearly related to x, then we can set the following equation:
[tex]C(x)=mx+b\text{.}[/tex]
To determine the values of m and b we will use the fact that:
[tex]\begin{gathered} C(43)=5075, \\ C(118)=10700. \end{gathered}[/tex]
Therefore we can set the following system of equations:
[tex]\begin{gathered} m\cdot43+b=5075, \\ m\cdot118+b=10700. \end{gathered}[/tex]
Subtracting the second equation from the first one we get:
[tex]\begin{gathered} m\cdot118+b-m\cdot43-b=10700-5075, \\ 75m=5625. \end{gathered}[/tex]
Dividing the above equation by 75 we get:
[tex]\begin{gathered} \frac{75m}{75}=\frac{5625}{75}, \\ m=75. \end{gathered}[/tex]
Substituting m=75 in 43m+b=5075, and solving for b we get:
[tex]\begin{gathered} 43\cdot75+b=5075, \\ b=5075-43\cdot75, \\ b=1850. \end{gathered}[/tex]
Therefore:
[tex]C(x)=75x+1850.[/tex]
B) Evaluating C(x) at x=123 we get:
[tex]\begin{gathered} C(123)=75\cdot123+1850, \\ C(123)=11075. \end{gathered}[/tex]
C) From the equation we get that the fixed cost is $1850.
D) The cost to produce each additional refrigerator is $75.
Answer:
(a)
[tex]C(x)=75x+1850.[/tex]
(b) $11075.
(c) $1850.
(d) $75.
