Question

The Diversified Vegetable Company grows two crops, tomatoes and zucchini. The firm is a price-taking seller. The price of a bushel of tomatoes is $20, while the price of a bushel of zucchini is $30. The firm uses the same land and the same workers to raise the two crops, and its total cost for the two crops is 5XT² + 6XZ² + XTXZ, where XT and XZ are the respective quantities of tomatoes and zucchini.

Find the following
A) The profit maximizing level of production of tomatoes and zucchini.
B) The maximized profits.

Answer 1

To find the profit-maximizing level of production of tomatoes and zucchini, equate the price to the marginal cost for each crop. The maximized profits can be calculated as the difference between total revenue and total cost.

Step-by-step explanation:

The profit-maximizing level of production of tomatoes and zucchini can be determined by finding the quantity where the price equals the marginal cost for each crop. In this case, Price = MR = MC. Let's assume the profit-maximizing quantities for tomatoes and zucchini are XT and XZ respectively. The formula for total cost is 5XT² + 6XZ² + XTXZ. The maximized profits can be calculated as the difference between total revenue and total cost.

Profit maximization arises when the derivative of the profit function with respect to an input is zero. This property is known as a first-order condition. Profit maximization arises with regards to an input when the value of the marginal product is equal to the input cost.

Profit maximisation is a process business firms undergo to ensure the best output and price levels are achieved in order to maximise its returns. Influential factors such as sale price, production cost and output levels are adjusted by the firm as a way of realising its profit goals.