A company has determined that the price and the monthly demand of one of its products are related by the following equation: Q = 400 – p. The associate d fixed costs are $2,000 per month and the variable costs are $100 per unit. What is the maximum profit? What is the range of profitable demand?
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For each of the following problems, (a) draw the cash flow diagram (as needed); (b) present clean and clear manual solutions to the problem; (c) highlight the final answer (only the final answer as required by the problem) by enclosing it within a box.
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- Calculate total revenue of a firm given that:- Profit = $500 Total cost = $1100A 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…What is relationship between total revenue (TR) and cost (TC) if the price is greater than ATC (is TR greater, less, or equal to TC)? Does the firm make positive economic profit or loss?
- (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 зFind average revenue if total revenue is $4400 and output is 22X 1 ences If the price of oats is $3.0 per kilo, calculate the total revenue and the total profit (or loss) at the quantities shown in below table. If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers. Leave no cells blank - be certain to enter "0" wherever required. Mc Graw Hill Quantity (kilos) Total revenue Total cost Total profit $ 600 1800 $1,900 700 2100 $2,000 $ 800 2400 $2,400
- What would be the profit earned by the firm if his total revenue is $490 and the total costs are $500Jeremy worked at a bank with a monthly salary of $1,500. He decided to quit his job and open a bookstore inhis neighborhood. He now pays $500 in rent, $80 in utilities and $120 in wages every month. He also paysthe publisher $5 per book sold. This month Jeremy sold 100 books at the price of $30 per book.a. What was the total revenue this month? Calculate this month’s explicit fixed cost, the variable costand the total cost.b. How much accounting profit did Jeremy make?c. How much economic profit did Jeremy make?d. If Jeremy had not quit his job at the bank, he could have been promoted and got a pay raise of 30percent. How would this affect his accounting profit and his economic profit?6. esc A company sells one of its products for $42 each. The monthly fixed costs are $2700. The marginal cost of the product is $10. Let q=quantity and C(q) = cost. a) Express the total monthly costs, C, as a function of q, the quantity produced each month. C(q) = 9= :0: 21 O Express the total monthly revenue, R, as a function of the quantity, q, sold each month. R(q) = c) Find the quantity, q, produced and sold each month at which this company will break even. Round your answer to a whole number. F1 50,252 8. F2 20 F3 ITEMS 000 000 F4 F5 INFO MacBook Pro S F6 tv F7 RA ► 11 F8 W < Previous Nex F9 Instructions ^ F10 4) F11 €
- The figure shows graphs of the total cost function and the total revenue function for a commodity. (Assume cost and revenue are measured in dollars.) y 500 400 300 200 100 MR 10 (a) Label each function correctly. function A ---Select--- function B ---Select--- (x, y): = 20 (b) Determine the fixed costs. $ 30 (c) Locate the break-even point. -([ = 40 50 Determine the number of units sold to break even. units A B 60 (d) Estimate the marginal cost MC and marginal revenue MR. MC = X(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?Tim Marlow, the owner of The Clock Works, wanted to know how many clocks he must sell in order to cover his fixed cost at a given price. Tim knew that he had a fixed cost of $20,000 for equipment, taxes, and a bank loan. He also had a unit variable cost of $20 per clock for labor, materials, and promotional costs. If the price Tim charges for each of his clocks is $40, what is his break-even point quantity?