The demand function for a company that produces and sells memory chips established the demand function as q = 100 – and total cost function as TC(q) = 2q² – 80q – 3200. Find the unit price at the break-even point. O A) 180 B) 80 O ) 10 D) 40 O E) 60

Q: The cost C for ordering and storing x units is C = 7x + 200,000/x. What order size will produce a…

A: Differentiate w.r.t to x

Q: The total revenue function of a firm is given as R = 21q – q² and it estimates the total cost…

A: Given, R = 21q-q2      1and c =13q2-3q2-7q+16    2for maximum and minimum,first find critical…

Q: Suppose the demand for a product is q = 1080 – 0.1 p. Determine the price, p, that results in…

A:

Q: Jollibee estimates that when r units of Peach Mango Pie are produced, the total cost will be C pesos…

A:

Q: A bicycle dealer has found that if 10-speed bicycles are sold for æ dollars apiece and the price of…

A: The solution is given below:

Q: Assume that it costs a manufacturer approximately C(x) = 800,000 + 340x + 0.0005x2 dollars to…

A: In this question, optimization technique is used. Optimization Technique using maxima and minima The…

Q: The demand function for a certain brand of compact discs is given by p = -3x2 -5x + 105 where p is…

A:

Q: The relationship between sales S and the amount x and y spent on two advertising media is given by…

A: Given: S=200x5+y+100y10+y To find: Solution

Q: A worker is to construct an open rectangular box with a square base and a volume of 98 ft°. If…

A:

Q: Determine the minimum cost of a retailer of motorized bicycles whose cost function is C(q) = 4860/q+…

A: Here the given cost function is: C(q)=4860q+15q+750000

Q: An oil refinery is located on the north bank of a straight river that is 1 km wide . A pipeline is…

A:

Q: Suppose that the labor cost for a building is approximated by C(x,y) = 4x2 + 3y2- 120x - 240y +…

A: We have to find the minimum labor cost.

Q: Suppose that the manufacturing cost of a particular item is approximated by M(x, y) = 6x³ x³y² +…

A:

Q: ) be the cost to produce x batches of widgets, and let R(x) be the revenue in thousands ars.…

A: Given: The cost to produce x batches of widgets is Cx=x+14 The revenue is Rx=-x2+10x C(x) and R(x)…

Q: Find the minimum cost of producing 50,000 units of a product, where x is the number of units of…

A:

Q: A worker is to construct an open rectangular box with a square base and a volume of 128 ft. If…

A:

Q: The monthly marketing and automated equipment cost (in millions of dollars) for a car company is…

A:

Q: A power line is to be constructed from a power station at point A to an island at point C, which is…

A: CB= 3 mi (underwater) AB= 4 mi (underground)  Cost to lay the power line under water = $3300 per…

Q: What would be the optimal location for a warehouse (minimum transportation distance) which would…

A: In order to find the optimal location for warehouse, we have to find the centre of mass w.r.t the…

Q: The cost C (in dólares) of ordering and storing x unit is C=2x+300,000/x. What order size will…

A: C=2x+300000xC represents cost and x represents storing unit.

Q: Find the relative maximum and minimum values. f(x,y) = 3x² – 4y?

A:

Q: Find all equilibrium points and determine their types when C =1. *, = x2 *, = -bx, +1+ c(-1+ sat…

A: Given: x.1=x2x.2 =-bx2+1+c-1+sat0.5-x1-x2

Q: The relationship between sales S and the amount x and y spent on two advertising media is given by…

A: Here, the sales, S is related to the amount x and y spent on two advertising media as follows:…

Q: A worker is to construct an open rectangular box with a square base and a volume of 128 ft, If…

A:

Q: An open top rectangular tank with square bases is to have a volume of 10 cubic meters. The material…

A: To find out the most economical height.

Q: The fuel-cost functions for the three thermal plants is $/h are given by C, = 400 + 5. 5P, + 0.006P…

A: The given constraint: 50≤P1≤15050≤P2≤20050≤P3≤300 Where P1, P2, P3 are the loads of the generator…

Q: D If C) = 16,000 +2001 +*4x5 in dollars, find ) the cost, avera qe cat , and marg inal cost at a…

A: The change in the total cost, when an additional unit of the product is sold is called the marginal…

Q: If a resistor of R ohms is connected across a battery of E volts with internal resistance r ohms,…

A:

Q: Given the Total Cost function, TC = 10 + 5Q?, find the marginal cost function, MC when Q = 10. [2]

A:

Q: Find all equilibrium points and determine their types when C = 1. * = x, *, = -bx, +1+c(-1+ sat…

A: Given: x.1=x2x.2=-bx2+1+c-1+sat0.5-x1-x2

Q: For y> 0, find the minimum value of + 10 +5y2 5 y2

A:

Q: Suppose that the manufacturer of a gas clothes dryer has found that when the unit price is p…

A:

Q: An open top rectangular tank with square bases is to have a volume of 10 cubic meters. The material…

A:

Q: The CMO of ABC Company presumed that the demand for a Product Y can be modeled by p=80-0.01y where p…

A: Maximum profit will occur at that value of x when derivative of profit function is zero. We will…

Q: The minimum value of Df(z, y) is ||Vf(z, y)||- Select one: O True O False

A:

Q: Assume that it costs Apple approximately C(x) = 25,600 + 100x + 0.01x² dollars to manufacture x 32GB…

A: We use second derivative test to find out minimum average cost

Q: A manufacturer of automotive shock absorbers is interested in comparing the durability of its shocks…

A:

Q: Assume that the demand curve is P = f(Q) = 60 − 0.2Q and the supply curve is P=g(Q) = 30 + 0.3Q.…

A:

Q: Let C(x) be the cost to produce x batches of Complete parts (a) through (d) below

A:

Q: Find the quantity which maximizes profit if the total revenue is given by R(q) = 5q – 0.003q²and…

A:

Q: Assume that a product has a profit function as: II(p, d) = 84d ¢ 400965 + 4752p 176 where p is price…

A:

Q: Suppose that the manufacturer of a gas clothes dryer has found that when the unit price is p…

A: Given equation - R =-4p2+4000p          ...........(1)Part (a) - Revenue = R = 0p = price = ?From…

Q: Given the following total revenue (TR) and total cost (TC) functions for a firm, TR = 5820Q + 40²…

A: Given that: Total revenue function is TR=5820Q+4Q2-2Q3+55 and the total cost function is…

Q: Use Cramer's rule to solve for P P, and P 0.5P +11.6P, – 8P, = -47.39 1.9P, +4.5P, = 59.94 0.8P+3.5P…

A: Solving p1,p2 and p3 by using cramers method:

Q: All consumens share a common valuation of 50 and face (there and back) transport costs of t0 per…

A: 40 is the correct answer that is the option c

Q: A baker can sell as many baguettes as he chooses for $2 per loaf. He estimates his cost in dollars…

A:

Q: The monthly marketing and automated equipment cost (in millions of dollars) for a car company is…

A:

Q: Find the consumer and producer surpluses (in dollars) by using the demand and supply functions,…

A:

Q: Find the local minimum value of f(r, y) = 4+ a7 + y7 – 7xy.

A: We need to find the local minimum of the equation.

Q: Given the total cost function for a St Lucian Construction Company is: TC = 1250 + 10Q-0.9Q2 + 0.06…

A: Given : TC = 1250 + 10Q - 0.9Q2 + 0.06Q3   To find :  a. Rate of output that results in minimum…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.