Find the required sum. 6 E ((k - 1)4 + 8) k= 1 6 2 ((k - 1)4 + 8) = (Simplify your answer.) k = 1

The equation p(x)= −40?^2 + 8000? − 250000 takes x, the number of items produced of a particular new consumer electronic device, and gives P, the profit generated for the manufacturer (in thousands of dollars). Determine the maximum profit.

is the following statement true if f(x) = (-2)x, then f(a-1)/f(a-4) = 8

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

The function P(x) - 1.25x² + 775x - 7000 gives the profit when x units of a certain product are sold. Find a) the profit when 85 units are sold = dollars b) the average profit per unit when 85 units are sold dollars per unit c) the rate that profit is changing when exactly 85 units are sold dollars per unit d) the rate that profit changes on average when the number of units sold rises from 85 to 170. dollars per unit e) The number of units sold when profit stops increasing and starts decreasing. (Round to the nearest whole number if necessary.) units

For the following problem, what would be the objective function that aims at minimizing the total cost considering that X1, X2, X3, and X4 are the number of units produced and sold of Products 1, 2, 3, and 4, respectively? Manufacturing time (hr) per unit Machine Cost per hr ($) Product 1 Product 2 Product 3 Product 4 Capacity (hr). 10 2 4 2 500 5 3 1 2 380 4 7 1 450 Unit selling price ($) 75 45 O a. 20X1+30X2+40X3+20X4 O b. None of the answers OC. 75X1+70X2+55X3+45X4 Od. 63X1+52X2+53X3+34X4 123 دي دا فيا 70 2 55

3. Minimize the following total cost function: TC = Q³ – 10Q2 + 48Q + 46.

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Needed to be solved correctly in 10 minutes and get the thumbs up please show neat and clean work Please do in 10 minutes only

Determine the returns to scale for the following production functions. a) ? = K + 7L b) ? = KL3