Question

A company decides to begin making and selling computers. The price function is given as follows:

p=−35x+2300,

where xx is the number of computers that can be sold at a price of pp dollars per unit. Additionally, the financial department has determined that the weekly fixed cost of production will be 3000 dollars with an additional cost of 150 dollars per unit.
(A) Find the revenue function in terms of x.
R(x)=

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(B) Use the financial department's estimates to determine the cost function in terms of x.
C(x)=

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(C) Find the profit function in terms of x.
P(x)=

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(D) Evaluate the marginal profit at x=250

Answer 1

Caven price function (P) = -35% + 2300 A Revenue fonction - (price fonction) (no-of units). » RCX) = (P) (x) BROVO) - (-35% +2300) 02) R(X) = 1-35x² +2300x Total cost cost coo) = fixed cost + variable o profit Here fixed cost = 3000 dollars variable cost = (no. of units) Cadditional cost per unit) = (x) (150) = 150%. CCX) = 13000 + 150x v e profit fundion poc) = Revenue RCO) - Cost cox) POC) = -3522 +2300X - (3000 + 150x] = -350² +23001 - 3000 - 150x pox) = -35x² + 2150 x - 3000 v o marginal profit = plcx) pl (x)= a [Px)] = a[ - 35 x ² + 2150 x - 3000] ' n -35 (2x) +2150 C1) - p'(x) = - 70x + 2150 /

plas 1₂. 250 - (-10x + 2150) | x = 250 = -70(250) +2150 - 17500 +2150 - 15350 marginal profit at &x=250) = [-15350] ✓