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- A cell phone factory has a cost of production C(x) = 150x + 10,000 and a revenue function R(x) = 200x. What is the break-even point? (x, R(x)) =1. Find the first and second derivatives a) y=((4x^3)/3) -x +2e^x b)y=6x^2-10x-5x^-2The demand function for a product under pure competition is p = (64 - 4x)1/2 and the supply function is p = x - 1, where x is the number of units and p is in dollars. Find the producer's surplus at market equilibrium.
- The average cost function for the weekly manufacture of retro portable CD players is given by C(x) = 120,000x−1 + 20 + 0.0002x dollars per player, where x is the number of CD players manufactured that week. Weekly production is currently 4,000 players and is increasing at a rate of 500 players per week. What is happening to the average cost?The total cost of producing a commodity is given by C = 60x^2 − 0.01x^3, where x is the numberof units produced. Determine the value of x so that the average unit cost is maximum.a. 3,000 unitsb. 4,000 units c. 300 unitsd. 2,500 units e. 5,000 unitsf. 0 unitsIsn't this a Bernulli equation: y'+p(x)y=q(x)y^n --> y'=q(x)y^n - p(x)y y'-y/x = x^3 (y-x)^2 --> y'=x^3 (y-x)^2 +y/x
- The demand and supply functions for a product are modeled by Demand: p = −0.2x + 8 and Supply: p = 0.1x + 2 Where x is the number of units in millions. Find the consumer and producer surpluses for this product.Solve for Elimination of Arbitrary constant given problem is x^2y=1+cx c is the arbitrary constantThe Cost function C(x) and the Revenue function R(x) of a firm are given by C(x) = 4x +1200 and R(x) = 10x, respectively. What is the firm's profit/loss when it produces and sells 100 units?
- The total-revenue and total-cost funtions for producing x clocks are R(x)=500x-0.01x2 and C(x)=160x+100,000, where x is greater than equal zero and less than equal 25,000. What is the maximum annual profit?The total cost of producing 1 unit of a product is given by C(x,y)=30+10x2+20y-xy dollars Where x is the hourly labor rate and y is the cost per pound of raw materials. the current hourly rate is $15 and the raw materials cost $6 per pound. how will an increase of a)$1 per pound for the raw materials affect the total cost b)$1 in the hourly labor rate affect the total cost?f(x)=(-0.7x2+6.8x+4.2)e-x^2 Find the critical points, inflection points and intercepts (if any) limits as x --> +/- infinity