Vincent makes dining tables, and he is trying to decide how many tables to produce. He can sell each dining table for $2,000. The cost of the first table is $750, and for the second it's $1,000. For each additional table he produces, the marginal cost of each table increases by $250. How many dining tables should Vincent produce, and what is the total cost of his production?
A)He will produce four tables at a cost of $4,500.
B)He will produce five tables at a cost of $6,250.
C)He will produce six tables at a cost of $8,250.
D)He will produce seven tables at a cost of $10,500.

Question

Quizplus · Accepted Answer

To find the optimal number of tables to produce, we need to compare the marginal revenue (MR) and marginal cost (MC) of each additional table. First, let's find the equation for MC: MC = $750 + ($250 x number of tables produced - 1) For example, when 3 tables are produced, the MC will be: MC = $750 + ($250 x 2) = $1,250 Now, let's find the equation for MR: MR = $2,000 Since MR is constant at $2,000, we don't need to consider the number of tables produced for MR. To find the optimal quantity, we need to compare the additional revenue earned from producing one more table (MR) to the additional cost of producing that table (MC). If MR > MC, then producing one more table will increase profit. If MR < MC, then producing one more table will decrease profit. If MR = MC, then profit is maximized at the current level of production. Let's calculate the MC and MR for each possible quantity: - 1 table: MC = $750 MR = $2,000 MR > MC, so producing one table is profitable. - 2 tables: MC = $1,000 MR = $2,000 MR > MC, so producing two tables is profitable. - 3 tables: MC = $1,250 MR = $2,000 MR > MC, so producing three tables is profitable. - 4 tables: MC = $1,500 MR = $2,000 MR > MC, so producing four tables is profitable. - 5 tables: MC = $1,750 MR = $2,000 MR > MC, so producing five tables is profitable. - 6 tables: MC = $2,000 MR = $2,000 MR = MC, so profit is maximized at producing six tables. - 7 tables: MC = $2,250 MR = $2,000 MR < MC, so producing seven tables would decrease profit. Therefore, Vincent should produce six tables to maximize profit. Total cost = $750 + $1,000 + $1,250 + $1,500 + $1,750 + $2,000 = $8,250

Vincent Makes Dining Tables, and He Is Trying to Decide