Provide an appropriate response.
-A snowboard company has manufacturing costs given by the equation $$C = \frac { \mathrm { Tx } + 1000 \mathrm {~T} } { \mathrm { x } }$$ where T is a different constant for each model, x is the number of snowboards manufactured, and C is the cost to manufacture one snowboard of a particular model. Choose which of the following statements are true with
Regard to this mathematical model.
I. The manufacturing cost per snowboard is the same for all models if 8000 of each model is manufactured.
II. The manufacturing cost per snowboard decreases for all models as the number manufactured increases.
III. The manufacturing cost per snowboard decreases for only some models as the number manufactured increases.
A) Only II is true.
B) All three statements are true.
C) Only I and III are true.
D) Only I and II are true.

Question

Quizplus · Accepted Answer

The cost per snowboard, $C$, decreases as $x$ increases, regardless of $T$, because the term $\frac{1000T}{x}$ becomes smaller. Statement I is false because $T$ affects the cost differently for each model. Statement III is false because the decrease in cost per snowboard applies to all models as $x$ increases, not just some.

Provide an Appropriate Response C=Tx+1000 TxC = \frac { \mathrm { Tx } + 1000 \mathrm {~T} } { \mathrm { x } }C=xTx+1000 T​

Provide an Appropriate Response $C = \frac { \mathrm { Tx } + 1000 \mathrm {~T} } { \mathrm { x } }$