A small manufacturing firm has two products that are produced using its in-house 3-D printers. The budget and time constraints for this process give the production possibilities curve defined by the table below. If the company is currently producing 30 units of product [tex]A[/tex] and 39 units of product [tex]B[/tex], can the production of product [tex]B[/tex] be increased? Explain.

\begin{tabular}{|l|c|c|c|c|c|c|c|}
\hline
Product A & 0 & 10 & 20 & 30 & 40 & 50 & 60 \\
\hline
Product B & 51 & 50 & 46 & 39 & 29 & 16 & 0 \\
\hline
\end{tabular}

(1 point)

A. No, the point is already on the production possibilities curve.
B. Yes, the production of product [tex]B[/tex] can be increased to whatever value is desired.
C. Yes, the production of product [tex]B[/tex] can be increased up to 51 by decreasing the volume of product [tex]A[/tex].
D. Yes, the production of product [tex]B[/tex] can be increased up to 60 by decreasing the volume of product [tex]A[/tex].



Answer :

Let's analyze the given production possibilities curve and the current production levels. The table below shows the production possibilities:

[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|} \hline \text{Product A} & 0 & 10 & 20 & 30 & 40 & 50 & 60 \\ \hline \text{Product B} & 51 & 50 & 46 & 39 & 29 & 16 & 0 \\ \hline \end{array} \][/tex]

According to the table, when the company produces 30 units of Product A, the maximum number of units of Product B that can be produced is 39. The current production level is 30 units of Product A and 39 units of Product B.

To determine if the production of Product B can be increased, we need to check if 39 units of Product B are the maximum possible for the given production level of 30 units of Product A.

Observations:
- For 30 units of Product A, the corresponding value in the table for Product B is 39 units.
- The table shows that when producing 30 units of Product A, the firm is already producing the maximum possible amount of Product B, which is 39 units.

Because 39 units of Product B is already the highest production level achievable when producing 30 units of Product A, it is not possible to increase the production of Product B without reducing the production of Product A.

So, the correct answer is:

No, the point is already on the production possibilities curve.