The demand function p=-4 +550 describes the relation between the number of televisions sold per week given by q, at a price of p dollars each. The weekly cost function is given by c=6800+150q. c) For which q will the marginal revenue be zero?

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4. (10 marks) The publisher Entertainment Arbitrator sells the popular video game Sprockets of Peace. When each copy of the game is priced at $40, the weekly demand is 8000 copies. For every $1 increase in price, the number sold per week decreases by 50. Assume that it costs $20 to produce each copy of the game. (a) Find the linear demand equation. Use p for the unit price and q for the weekly demand (b) Find the weekly cost function C(q) as a function of q. (c) Find the weekly revenue function R(q) as a function of q.

75 9. A marketing researcher has determined that when a product sells at a dollars per unit, the number of units sold per week is given by the function q = - + 80(5m - 2) where m>O is the total manufacturing cost in dollars per unit and m < x < 5m. 2 m (a) Find the profit function P(x) (in dollars per week) and simplify it. (5 points) (b) Use calculus to find the selling price x that maximizes weekly profit. Sufficiently justify your solution. [6 points] (c) Use your answer to part (b) to determine the manufacturing cost m that yields a maxi- mum weekly profit of 3, 455 dollars. [4 points)

8. A company is planning to produce a new electric toaster. After conducting an extensive market survey, the research department provides the following information: when the unit price is $16 per toaster, then the weekly demand is 20 toasters; for every $2 decrease in the unit price, the weekly demand increases by 10 toasters. The financial department estimate that the weekly fix costs will be $140 and the variable cost of production will be $4 per toaster. Let p be the unit price and let q be weekly demand. Note: Please simplify your answers such that your answers for (b) and (c) are given by integers. (a) Find the demand function linking p and q. Answer:

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The demand function p=-4 +550 describes the relation between the number of televisions sold per week given by q, at a price of p dollars each. The weekly cost function is given by c=6800+150q. c) For which q will the marginal revenue be zero?

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