SOLUTION: The demand equation for a certain product is given by p=108-0.001x, where p is the unit price(in dollars) of the product and x is the number of units produced and sold. The cost eq
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Question 998203: The demand equation for a certain product is given by p=108-0.001x, where p is the unit price(in dollars) of the product and x is the number of units produced and sold. The cost equation for the product is C=85x+150,000, where C is the total cost(in dollars) and x is the number of products produced and sold. The revenue equation for the product is R = xp, where R is the total revenue(in dallars), p is the unit price (in dallars), and x is number of products produced and sold.
1. what is maximum profit P?
2. what is the unit price p that produces the maximum profit P?
3.if a pfofit of 9 million is possible, what is unit price P?
if a profit of 9 milloin is not possible, explain why?
4. what is the minimum unit rice P that can be used so that the company does not lose money?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
1.
\ =\ 85x\ +\ 100,000)
\ =\ x(108\ -\ 0.001x)\ =\ 108x\ -\ 0.001x^2)
\ =\ R(x)\ -\ C(x))
Substitute the functions, collect like terms, and then use the formula for the vertex of a parabola or take the first derivative to find the local maximum of the function.
John
My calculator said it, I believe it, that settles it
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