A company is planning to manufacture and market a new four-slice toaster. For th

Question

A company is planning to manufacture and market a new four-slice toaster. For this toaster, the research department's estimates are a weekly demand of 300 toasters at a price of $25 per toaster and a weekly demand of 400 toasters at a price of $20. The financial department's estimates are fixed weekly costs of $5000 and variable costs of $5 per toaster.

(a). Assume that the relationship between price p and demand x is linear. Use the research department's estimates to express p as a function of x, and find the domain of this function.

(b). Find the revenue function R(x) from the sale of x pairs of running shoes, and state its domain.

(c). Evaluate the marginal revenue at x=325 and x=425 and interpet the results.

Please show work, Thank you!

Explanation / Answer

Since there is a relation between and is linear and is a function in .

At , and at , .

Thus, the of the linear curve (line) is,

The equation of the line is,

Here, for all .

Thus,

Therefore, the domain of the function is .

The revenue function is defined by,

Here, also is function depend on , then the domain of this function also

.

The cost function is linear with fixed costs of $5000 and a variable cost of $5 per toaster gives,

Thus, the profit function is,

The marginal revenue is,

At ,

At ,

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