5. Let U(x, y) be the utility function for two goods, X and Y, given by xy² x- Y U au au Find the marginal utility of each product. That is find and ?х ду You must simplify the numerator in your final answers.
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- A company has two plants that produce the same lawn mower. If x1 and x2 are the numbers of units produced at plant 1 and plant 2, respectively, then the total revenue for the product is given by R = 300x1 + 300x2 − 5x21 − 10x1x2 − 5x22 . When x1 = 5 and x2 = 8, find (a) the marginal revenue for plant 1, ∂R/∂x1, and (b) the marginal revenue for plant 2, ∂R/∂x2.The marginal cost function for Company A is C'(q)=q^2-8q+40 dollars/unit where q is the quantity producded. If C(0)= 500, then 1) what is the fixed cost in dollars? 2)Using a calculator or fundamental theorem, compute the total variable cost of producing 30 units 3) What is the total cost of producing 30 units?If the utility function of an individual takes the form U=U(x1,x2 )=(x1+2 )2(x2+3)3 Where U is total utility, and x1 and x2 are the quantities of two commodities consumed:i. Find the marginal utility function of each of the two commodities.ii. Find the value of the marginal utility of the first commodity when 3 units of eachcommodity are consumed.
- Suppose the revenue function for polka dot widgets is given by R(q)=−6q2+700q , where R(q) is in dollars and q is the number of widgets sold. Find a numeric value for the marginal revenue at 47 units, and record your result in the box below. Answer: MR(47)= $perunitRound your answer to the nearest dollar. [Note: you are being asked to solve for the Marginal Revenue, not the optimal number of widgets to maximize revenue]Suppose a product's revenue function is given by R(q)=−8q2+1000qR(q)=-8q2+1000q , where R(q)R(q) is in dollars and qq is units sold.Find a numeric value for the marginal revenue at 1010 units, and record your result in the box below.Suppose a product's revenue function is given by R(q)=−5q^2+800q, where R(q) is in dollars and q is the number of units sold. use the marginal revenue function to find the approximate revenue generated by selling the 27th unit. _______$ per unit.
- A small tie shop finds that at a sales level of x ties per day its marginal profit is MP(x) dollars per tie. where MP(x) = 1.25 + 0.10x - 0.0006x^2 Also the shon will lose $75 per dav at a sales level of x= 0. Find the profit from operating the shoo at a sales level of x ties per daySuppose that the marginal revenue from the sale of x units of a product is MR = R'(x) = 3e0.01x. What is the revenue in dollars from the sale of 100 units of the product?Suppose a product's revenue function is given by R(q)=−6q^2+200q, where R(q)is in dollars and qq is units sold. Find a numeric value for the marginal revenue at 27 units. MR(27)=_____
- 3. The joint cost (in thousands of euros) for two products X and Y can be given by the following formula: C(x, y) = 40 + y^2 + 3x + 2xy + (x^2) y + y^3 where x represents the quantity of product X that is produced and y represents the quantity of product Y produced. • If 12 units of product X and 20 units of product Y are produced, what are the marginal costs? • What product line should be expanded in the current level of production?McRoberts Electronics sells 200 TVs per month at a price of $400 per unit. Market research indicates that the store can sell one additional TV for each $1 it reduces the price. In this case the total revenue function is given by where is the additional TVs beyond the 200. If the store sells a total of 250 TVs, then find the marginal revenue.If the revenue function for a certain commodity is R(x) = 45x/lnx compute the marginal revenue when x = 40.