U = 5x11/2 + 2x2. What is the marginal rate of substitution at (1, 4)? Round your answer to two decimal places.

Write the technical rate of substitution expression for f(x1, x2) = (x1 - 1)0.25 x20.5

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A sheet of paper 80 cm-by-72 cm is made into an open box (i.e. there's no top), by cutting x-cm squares out of each corner and folding up the sides. Find the value of x that maximizes the volume of the box. Give your answer in the simplified radical form. X = is the max.

If Fred's MRS of salad for pizza equals -5 (where salad is on the vertical axis), then which of the following is True? He will eat 5 times as much pizza as salad He would give up 5 salads to get the next pizza He will eat 5 times as much salad as pizza He would give up 5 pizzas to get the next salad x

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Solve part a and b of question. Please show all steps and explain. Note: it’s a optimization problem

Given the following values:  P(A) = 0.25    P(A and B) = 0.14     P(B) = 0.32  Find the P(B | A) (Leave answer in decimal form with 2 decimals)

Revenue R from the sale of x units of a product is found by multiplying the price by the number of items sold. (a) Factor the right side of R = 200x - x². R = (b) What is the expression for the price of the item? The consumer expenditure, in dollars, for a commodity is the product of its market price, p, and the number of units demanded, x. Suppose that for a certain commodity, the consumer expenditure is given by 9,000p - 150p². (a) Factor this in order to find an expression for the number of units demanded. (Simplify your answer completely.) x = units (b) Use (a) to find the number of units demanded when the market price is $33. x = units A company's average cost per unit when x units are produced is defined to be Total cost Average cost = Χ Suppose a company's average costs are given by 6000 Average cost = +35+0.2x. X Express the average-cost formula as a single fraction. Average cost = 3

Consider the following graph of y = f(x). E D A Which of the following statements about the function f is true? Select one: O f has an endpoint at E and a y-intercept at B. O f has a global maximum at A and a global minimum at C. O f has a critical point at C and a global minimum at D. O f has a global minimum at A and a y-intercept at D.