1) The demand equation for your company’s virtual reality video headsets is
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.
What is the greatest profit your company can make in a week? (Give your answer to the nearest whole number.)
How many headsets will your company sell at this level of profit? (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?