The price demand and profit functions for selling x items of a newly introduced perfume are given by p(x) = 50x100 and P(x) = 30x² 20x + - 10000 x² 20000 X respectively. Approximate the cost of producing the 11th perfume.
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- A local company is planning to manufacture and market a four-slice toaster. For this toaster, the research department’s estimates are aweekly demand of 300 toasters at a price of $25 per toaster and a weekly demand of 400 toasters at a price of $20. The financial department’s estimates are fixed weekly costs of$5,000 and variable costs of $5 per toaster. a) Assume that the relationship between price ? and demand ? is linear. Use the research department’s estimates to express ? as a function of ? and determine the domain of the function. b) Using your knowledge from Finite Math, determine the Revenue function in terms of ?. c) Determine the Marginal Revenue at 2 different production levels for example 250 and 500 units. Interpret these results. (HINT: Consider what a positive or negative first derivative implies) d) Assume that the cost function is linear. Use the financial department’s estimates to express the cost function interms of ?. e) Determinethe Marginal costand interpret the…A local newspaper currently has 84,000 subscribers at a quarterly charge of $30.Market research has suggested that if the owners raise the price to $32, they wouldlose 5,000 subscribers. Assuming that subscriptions are linearly related to theprice, what price should the newspaper charge for a quarterly subscription tomaximize their revenue?a) Find the cost function (Hint: find slope and use point-slope form to find thecost function) b) Find the revenue function c) Find the maximum revenue d) Find the profit functionOn the following graph, use the green point (triangle symbol) to plot the weekly total revenue when the market price is $50, $75, $100, $125, $150, $175, and $200 per scooter. TOTAL REVENUE (Dollars) 2610 2430 2250 2070 1890 1710 1530 1350 1170 990 Δ ΔΔ Δ 0 25 50 75 100 125 150 175 200 225 250 275 300 325 PRICE (Dollars per scooter) Total Revenue ? According to the midpoint method, the price elasticity of demand between points A and B is approximately 0.69 ▼ Suppose the price of scooters is currently $125 per scooter, shown as point A on the initial graph. Because the demand between points A and B is inelastic , a $25-per-scooter decrease in price will lead to a decrease in total revenue per week.
- A manufacturer can produce a gizmo at a cost of $6 apice. He sells this gizmo for $10 ,and at this price 10 gizmos are sold each day. The manufacturer figures that each $3 dollars decrease in price will sell 3 additional goods each day. Write out the Demand and Profit functions. What price xmaximizes profit?The following graph illustrates the weekly demand curve for motorized scooters in Roanoke. Use the green rectangle (triangle symbols) to compute total revenue at various prices along the demand curve. Note: You will not be graded on any changes made to this graph. PRICE (Dollars per scooter) 260 240 220 200 180 160 140 120 100 80 60 40 20 0 0 9 18 27 A X B Demand 36 45 54 63 72 81 QUANTITY (Scooters) 90 99 108 117 Total Revenue ?The following graph shows the daily demand curve for bippitybops in Denver. Use the green rectangle (triangle symbols) to compute total revenue at various prices along the demand curve. Note: You will not be graded on any changes made to this graph. PRICE (Dollars per bippitybop) 240 220 200 180 160 140 120 100 80 8 60 40 20 0 mớ H + 0 9 18 27 36 45 54 63 72 81 QUANTITY (Bippitybops per day) * Demand 90 B 99 108 Total Revenue (?)
- 13. The marginal profit for the new X-99 pogo stick is P'(x) = -0.1x+ 60 where x is the number of sticks produced and sold. The profit is - $1000 when 50 sticks have been produce and sold. a) Find the profit function. b) What level of production of pogo sticks (x) produces a maximum profit?2. The relationship between price and demand per month for a consumer product is p = 3500 -1.1D5 where p is the price per unit in dollars and D is the demand in units. The fixed cost is $300 per month and the variable cost is $4.00 per unit. What is the optimal number of units that should be produced and sold per month? a. b. What is the maximum profit per month?(b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p = 40 – 4q²where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (i) Write an equation giving profit as a function of the number of lightweight compasses produced. (ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit? Problem з
- (a) At what output is the firm’s profit maximised and How much profit is made at this output? (b) Draw the total profit TΠ curve over the range of output where positive profit is made. (d) How much is total fixed cost, At what output is the price elasticity of demand equal to -1 and At what outputs does the firm break even?you are an accountant for a manufacterer of radios. the demand function for the tablets is p= 40-4x2 where x is the number of tablets produced in millions. it costs the company $15 to make a tablet. write an equation for the manufactures profit as a function of the number of tablets produced. the company currently produces 1 million tablets and makes a profit of $21000000, but you would like to scale up production a bit, what greater number of tablets could the company produce to yield the same profitA company has established that the relationship between the sales price for one of its products and the quantity sold per month is approximately p=60-0.1D (D is the demand or quantity sold per month and p is the price in dollars). The fixed cost is $2,000 per month and the variable cost is $20 per unit produced. a. What is the maximum profit per month for this product? b. What is the range of profitable demand during a month? COLL a. The maximum profit per month for this product is $. (Round to the nearest dollar.) BOX AI