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Given that consumer demand for a firm’s output can be expressed as

A manufacturer’s marginal revenue is:  MR = R’ = 45 – 4q. Use integration to find the additional revenue (R) earned by increasing sales from [x] to [y] units. Enter your answer as a whole number.

A firm faces a Cobb-Douglas production function of Q = 60KL. Determine the optimal bundle of capital and labor that minimizes the cost of producing 15,000 units, given that the price per unit of capital is r = $25 and the price per unit of labor is w = $10.

FashionFix, an online fashion retailer, offered an opportunity to pay only $30 for a $50 voucher to use on their site. 1000 new customers take advantage of this offer. This group of customers was then tracked over a 3-year period (t = 3). The average annual purchase was $500 with a gross margin of 50% and annual per capita marketing expense of $10. FashionFix uses a discount rate of 9% and the retention rate is 25%. Calculate the Customer Lifetime Value.Important: reflect on what the CAC is for FashionFix to issue this deal on the voucher. To receive any points for this question, you MUST show your work.   

In the article, “An Anthropologist Walks into a Bar”, X explains how the Danish medical technology firm Coloplast used sensemaking to understand why its new products were not “getting any traction”.  Explain: a) what research methods Coloplast had tried that did not result in successful product innovations (1 point); b) what sensemaking is — you don’t need to identify the 5 stages of sensemaking (2 points); and c) how Coloplast used sensemaking to understand its customers and the challenges they faced and to then create a product better suited to customer needs and lifestyles (2 points).  

Find the sum Sn of the first n terms of the geometric sequence. -8, -16, -32, -64, -128, . . . ; n = 9

Find the focus and the directrix of the parabola.(x + 2)2 = 16(y + 4)

Graph the hyperbola, the asymptotes, and the vertices of the fundamental rectangle. – = 1

Simplify the factorial expression.

Nematode worms and annelid worms share which of the following features?