A manufacturer of a new patented product has found that he can sell 70 units a week to the customer if the price is $48. In error, the price was recently advertised at $78 and as a result, only 40 units were sold in a week. The manufacturers fixed costs of production are $1,710 a week and variable costs are $9 per unit. You are required to: a. Show the equation of the demand function linking price (P) to quantity demanded (X) assuming it to be a straight line is P = 118-x
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A manufacturer of a new patented product has found that he can sell 70 units a week to the customer if the price is $48. In error, the price was recently advertised at $78 and as a result, only 40 units were sold in a week. The
a. Show the equation of the demand function linking price (P) to quantity demanded (X) assuming it to be a straight line is P = 118-x
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- A manufacturer of a new patented product has found that he can sell 70 units a week to the customer if the price is $48. In error, the price was recently advertised at $78 and as a result only 40 units were sold in a week. The manufacturers fixed costs of production are $ 1710 a week and variable costs are $9 per unit. You are required to a) Show the equation of the demand function linking price (P) to quantity demanded (X) assuming it to be a straight line is P = 118-xa textile company manufactures and sells x shirts per month. the monthly cost and price demand equations are given as C(x)= 150,000+30x and p = 50-x/100. using the analysis from obtaining the demand function and price elasticity of demand, discuss what the textile company can do to increase revenue from the sale of shirts.James mainly sells confectionery items, newspapers, magazines and cigarettes in his convenience store. Noting his small business is not thriving, he thought of selling hot pies and rolls too. Suppose the total cost function for rolls and pies is, TC = 900 + 50Q, Q = Q1 + Q2 Where Q1 and Q2denote the quantities of rolls and pies respectfully. If P1 and P2 denote the corresponding prices, the inverse demand equations are. Q1 = 70 - P1 and 0.5Q2 = 100 - P2 a)If James decides to make a total of 48 rolls and pies per day and charges different prices as above (that is, P1 ≠ P2 ), how many of rolls and pies each should he make in order to maximize the profit of a particular day? Estimate and interpret the Lagrange Multiplier λ [note: assume second-order conditions are satisfied]. b)Using your knowledge of input-output tables, explain which components of the economy will be affected if all convenience stores, including James’, closed down for three months due to the COVID-19. What would…
- Let the demand function for a product be given by the function D(q) = - 1.3q + 290, where q is the quantity of items in demand and D(q) is the price per item, in dollars, that can be charged when q units are sold. Suppose fixed costs of production for this item are $5, 000 and variable costs are $9 per item produced. If 192 items are produced and sold, find the following: A) The total revenue from selling 192 items (to the nearest penny). Answer: $ B) The total costs to produce 192 items (to the nearest penny). Answer: $ C) The total profits to produce 192 items (to the nearest penny. Profits may or may not be negative.). Answer: $When the admission price for a baseball game was $4 per ticket, 50,000 tickets were sold. When the price was raised to $5, only 45,000 tickets were sold. Assume that the demand function is linear and that the variable and fixed costs for the ball park owners are $0.10 and $95,000 respectively. (a) Find the profit P as a function of x, the number of tickets sold. P(x) = (b) Select the graph of P. y 150000 y 150000 150 000 100 000 100 000 100 000 50 000 50 000 50 000 20000 40 000 60 00p 20000 40 000 60 000 20000 40 000 60 000 - 50 000 -50 000 -50 000 -100 000 100000 100000 The xy-coordinate plane is given. The curve starts at the approximate point (0, 3,000), goes up and right becoming less steep, and exits the window at the approximate point o-150000 O o-150000L O O (70,000, 69,000). 150000 100 000. 50 000- 20000 40 000 60 do0 - 50 000 100 000- o 150 000Q2)Tony Keonte owns a factory that manufactures Eye-Games. His weekly profit (in thousands of dollars) is given by the following function: P(x) = -4x2 + 80x- 300. Where x is the number of Eye-Games sold. a) What is the largest number of Eye-Games that the company can sell and still make profit? (25 points) b) How many Eye-Games will the firm have to produce and sell in order to maximize profit? (25 points)
- Best Orange Juice Company is located in Oman. The cost function for total orange juice production (x) is given by C(q) 3D0.25x². Their orange juice is demanded only in Muscat (Muscat demand is Xm= 100-2Pm) and Salalah (Salalah demand is 100-4P,). Therefore, the total demand is x-St Xs. If the company can control the quantities supplied to each market, how many should it sell in each location to maximize total profits? What price would it charge in each location? AnswerE Let the demand function for a product be given by the function D(q) = -1.65g + 270, where q is the quantity of items in demand and D(q) is the price per item, in dollars, that can be charged when q units are sold. Suppose fixed costs of production for this item are $4, 000 and variable costs are $3 per item produced. If 96 items are produced and sold, find the following: A) The total revenue from selling 96 items (to the nearest penny). Answer: $ B) The total costs to produce 96 items (to the nearest penny). Answer: $ C) The total profits to produce 96 items (to the nearest penny. Profits may or may not be negative.). Answer: $ Question Help: C ME PE Video 66°F Mostly cloudyYou are an accountant for a manufacturer 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. (i). Write an equation for the manufacturer's profit as a function of the number of tablets produced. (ii). The company currently produces 1 million tablets and makes a profit of $21,000,000, but you would like to scale up production a bit. What greater number of tablets could the company produce to yield the same profit?
- (i) If the demand function for a particular commodity is p=−0.09x+51 and the total cost function C(x)=1.32x2+11.7x+101.4,where x is the level of production. Find (a) The revenue R(x) and profit Π(x). (b) All values of x for which production of the commodity is profitable. (ii) The total cost of manufacturing x units during the daily production run at a factory,is C(x)= x2+ x+900 dollars. Usually,x(t)=25t units are manufactured during the first t hours of production. (a) Express the total manufacturing cost as a function of t. (b) How much will have been spent on production by the end of the third hour? (c) When will the total manufacturing cost reach $11,000?The total cost and the total revenue (in dollars) for the production and sale of x ski jackets are given by C(x) = 28x + 20,160 and R(x) = 200x - 0.2x2 for 0sxs 1000. Find the value of x where the graph of R(x) has a horizontal tangent line. Find the profit function P(x). Find the value of x where the graph of P(x) has a horizontal tangent line. Graph C(x), R(x), and P(x) on the same coordinate system for 0 sxs 1000. Find the break-even points. Find the x-intercepts of the graph of P(x).A company manufactures and sells x cellphones per week. The weekly price-demand and cost equations are given below. p=600-0.1x and C(x)= 15,000+ 130x (A) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly revenue? What is the maximum weekly revenus? The company should produce phones each week at a price of $ (Round to the nearest cent as needed.) The maximum weekly revenue is S. (Round to the nearest cent as needed.) (B) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly profit? What is the maximum weekly profit? The company should produce phones each week at a price of $ (Round to the nearest cent as needed.) The maximum weekly profit is $ (Round to the nearest cent as needed.)