(i) The price p, in dollars, of a certain commodity and the quantity x sold obey the demand equation p = −1/5 x + 200 where 0 ≤ x ≤ 1000 Suppose that the cost C, in dollars, of producing x units is C =√x /10 + 400 Assuming that all items produced are sold, find the cost C as a function of the price p. (ii)The profit function, in dollars, for a product is given by Π(x) = −x 3 + 76x 2 − 380x − 2800, where x is the number of units produced and sold. If break-even occurs when 10 units are produced and sold, (a) Find a quadratic factor of Π(x). (b) Find a number of units other than 10 that gives break-even for the product.
(i) The price p, in dollars, of a certain commodity and the quantity x sold obey the demand equation p = −1/5 x + 200 where 0 ≤ x ≤ 1000 Suppose that the cost C, in dollars, of producing x units is C =√x /10 + 400
Assuming that all items produced are sold, find the cost C as a function of the price p.
(ii)The profit function, in dollars, for a product is given by Π(x) = −x 3 + 76x 2 − 380x − 2800,
where x is the number of units produced and sold. If break-even occurs when 10 units are
produced and sold,
(a) Find a quadratic factor of Π(x).
(b) Find a number of units other than 10 that gives break-even for the product.
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