Where q is the total number of headsets that your company can sell in

1)  The demand equation for your company’s virtual reality video headsets is

p =

where q is the total number of headsets that your company can sell in a week at a price of p dollars. The total manufacturing and shipping cost amounts to \$130 per headset.

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What is the greatest profit your company can make in a week? (Give your answer to the nearest whole number.)

How much, to the nearest \$1, should your company charge per headset for the maximum profit?

2) The number of cell phone subscribers in a country in the years 2000-2005 was projected to follow the equation

N(t) = 39t + 62

million subscribers in year t (t = 0 represents January 2000). The average annual revenue per cell phone user was \$350 in 2000. If we assume that due to competition the revenue per cell phone user decreases continuously at an annual rate of 20%, we can model the annual revenue as

R(t) = 350(39t + 62)e−0.2t million dollars.

Determine when to the nearest 0.1 year the revenue was projected to peak.

Determine the revenue, to the nearest \$1 million, at that time.

3) Fly-by-Night Airlines has a peculiar rule about luggage: The length l and width w of a bag must add up to at most 42 inches, and the width w and height h must also add up to at most42 inches. What are the dimensions of the bag with the largest volume that Fly-by-Night will accept?

4) I would like to create a rectangular vegetable patch. The fencing for the east and west sides costs \$4 per foot, and the fencing for the north and south sides costs only \$2 per foot. I have a budget of \$80 for the project. What are the dimensions of the vegetable patch with the largest area I can enclose?