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1. A company has determined that if the price of an item is $40, then 150...
1. A company has determined that if the price of an item is $40, then 150 will be demanded by consumers. When the price is $45, then 100 items are demanded by consumers (a) Find the price-demand equation, assuming that it is linear. (2 marks) (b) Find the revenue function. (1 mark) (c) Find the number of items sold that will give the maximum revenue. What is the maximum revenue? (4 marks) (d) What is the price of each item...
Problem 1: A company produces an item at a per-unit cost of $1000 and a fixed cost of $50,000. The selling price is a linear function of number of items demanded as follows: p = 15,000 - 200x, x5 80 A. Find the per-unit selling price when the demand is 30. B. Find the revenue function and find the revenue when the demand is 30. C. Find the cost function and find the cost when the demand is 30. D....
Problem 1: A company produces an item at a per-unit cost of $1000 and a fixed cost of $50,000. The selling price is a linear function of number of items demanded as follows: p = 15,000 - 200x, x5 80 A. Find the per-unit selling price when the demand is 30. B. Find the revenue function and find the revenue when the demand is 30. C. Find the cost function and find the cost when the demand is 30. D....
Q-6. Research shows that the demand function for a new product is d(x)-5x + 18, where x represents the number of items in thousands and d represents the item price in $.The cost function is C(x) 2x + 9 a. State the Revenue function R(x) [1 mark] b. Find the corresponding Profit function P(x). [1 mark] c. How many items must be sold to maximize profit? [2 marks] c.How many items must be sold for the company to break even?...
Based upon market research, the Hawthorne Company has determined that consumers are willing to purchase 133 units of their portable media player each week when the price is set at $46.20 per unit. At a unit price of $11.80, consumers are willing to buy 305 units per week. (a) Determine the weekly demand equation for this product, assuming price, p, and quantity, x, are linearly related. p (b) Determine the weekly revenue function. R(x) (c) Determine the number of units...
Question 2 [20 marks] = Given that the price of the product is P(Q) 4000 – 33Q and the Marginal Cost function of producing the same product is C' = 602 – 6Q + 400. Assuming Q> 0. a) Find the revenue and marginal revenue function of the production in term of Q. (3 Marks) b) Find the total cost function if the fixed cost of the production is RM5000. (4 Marks) c) Interpret the result of the marginal profit...
Need help with E-J. please :) Business Calc. Price-Demand Functions 2. The same outdoor company does some market rescarch and finds the following data estimating the number of people that are willing to buy the snowshoes at a certain price. For example, if the selling price of the snowshoes was $345, their estimates show that they would sell 50 pairs of snowshoes. of price pairs a) Create a scatterplot of the data using price as the dependent variable. snowshoes demanded...
In marketing a certain item, a business has discovered that thedemand for the item is represented by p=. The cost of producing x items isgivenby C = 0.4x + 1000.Find the following:Profit function P and the price per unit (rounded to thenearest whole cent) that yields a maximum profit.Profit function P = ________(this is the primary equationfor this optimization problem)feasible domain ofprimary equation: ___________(interval)the number of units _____ and the priceper unit that yield max profit: _____. (round to nearestwhole...
2. Units cost $0.50 each to produce an item and they sell for $3.00 each. The overhead in setting up production is $2,000. a) Find the cost and the revenue functions. b) Find the breakeven point. Also graph the cost and revenue functions and label the breakeven point. c) How many units must be sold to yield a profit of $2,000? d) Find the average profit function and the rate of change of the average profit when x=20 items.
A company has operating costs of $2000 per thousand items produced. Its revenue function can be modeled by the equation: R(x)=30x/(x+2)² , where x is measured in thousands of items produced, and C and R are measured in thousands of dollars (so C(x)=2).1. Determine the price-demand equation, solved for price.2. Determine the profit function, P(x)3. For what range of items does this company earn money?4. How many items should the company plan to produce in order to maximize profit?5. Determine...