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- A company has established that the relationship between the sales price for one of its products and the quantity sold per month is approximately p = 75 – 0.1D units (D is the demand or quantity sold per month and p is the price in dollars). The fixed cost is $1,000 per month and the variable cost is $30 per unit produced. Solve, a. What is the maximum profit per month related to thisproduct? b. What is the range of profitable demand during a month?The cost, in millions of dollars, of building a three-story high school in NewYork State was estimated to be: 2C x x x x 1.7 0.14 0.0001 20 400where x is the number of thousands of square feet. Suppose that you arecontemplating building a for-profit three-story high school and estimate thatyour total revenue will be $0.2 million dollars per thousand square feet.(a) What is minimum area for a three-story high school in New YorkState, that this model covers? (b) What is the variable cost of building a three-story high school in NewYork State? (c) What is the fixed cost of building a three-story high school in NewYork State? (d) Determine the profit function,P x( ), for building a three-story highschool in New York State? . (e) Determine,P(250) , for building a three-story high school in New YorkState, and interpret the result. (f) How many thousands of square feet should a three-story high schoolbuilding in New York State be in order to break even?It costs a baker a fixed cost of $420 and variable cost of $2.10 per cupcake. A cupcake is sold for $4.90 each. (iv) Write an algebraic expression representing the revenue R as a function of the number of cupcakes x sold.(v) Graph both functions on the same coordinate axes.(vi) From your graph find coordinatae at which cost equals revenue.(vii) Using your graph, determine how many cupcakes need to be made to produce revenue of at least $1,029. How much profit is made for this number of cupcakes?
- 1. (a) A company expects fixed cost of $55,000. Margin is to be 46 percent of the retail. Variable cost in addition to costs of goods is estimated at $0.06 per dollars of sale. Find the profit function using s for sales volume. (b) Square Hospital Limited charges every COVID patient a fixed amount for using their ICU facilities. What would be the graphical nature of the demand function of ICU in this case ? (c) Write down the general form of the Augmented matrix of a system of Linear Equation which consists of 5 equations and 4 unknowns. (0.5 0.5 (d) Calculate the steady state vector for the given transition matrix: (e) Assuming the nonnegativity constraints for each variables, calculate the total number of corner points for the following system of inequalities: 2x + 5y + 4z 2 29 3r + 2y + z 2 23 10r + 8y +5z > 62Until recently, hamburgers at the city sports arena cost $2.50 each. The food concessionaire sold an average of 4,500 hamburgers on game night. WWhen the price was raised to $3.00, hamburger sales dropped off to an averag of 4,000 per night. The concessionaire's fixed costs were $7,405.30 per night and the variable cost was $0.54 per hamburger. Answer the following questions (A) through (F). (A) Assume that the relationship between price p and demand x is linear. Express p as a function of x and find the domain of this function. ..... (Simplify your answer.) The domain of p is (Type a compound inequality.) (B) Find the revenue function in terms of x and state its domain. R(x) = (Simplify your answer.) The domain of R(x) is (Type a compound inequality.) (C) Assume that the cost function is linear. Express the cost function in terms of x. C(x) = (Simplify your answer.) (D) Graph the cost function and the revenue function in the same coordinate system. Choose the correct graph below. O A.…The following graph shows the daily demand curve for bikes in Houston. 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. 240 220 200 Total Revenue 180 160 140 120 100 80 60 40 20 0 PRICE (Dollars per bike) 0 9 18 27 > 36 45 54 63 72 QUANTITY (Bikes) 00 8 Demand 90 81 99 106
- The cost, in dollars, of producing x yards of a certain fabric is C(x) = 900 + 12x - 0.1x² +0.0005x³ and the company finds that if it sells x yards, it can charge p(x) = 27-0.00021x dollars per yard for the fabric. (a) Graph the cost and revenue functions. y 8000 6000 4000 2000 y 15 000 10 000 5000 R C 100 R =² C 100 200 200 300 300 X 400 400 X Use the graph to estimate the production level for maximum profit. 283.092 x yards y 15 000 10 000 5000 y 15 000 10 000 5000 R 100 R C 100 200 200 (b) Use calculus to find the production level for maximum profit. (Round your answer to two decimal places.) 186.63 yards 300 300 400 400 XSuppose that the marginal revenue for a product is MR = 900 and the marginal cost is MC = 33,(x+9), with %3D a fixed cost of $1434. Find the profit or loss from the production and sale of 5 units. A) loss of S735 B) loss of $13,010 c) profit of $13,010 D profit of $10,810 (E) loss of $10,810Consider the accompanying breakeven graph for an investment, and answer the following questions.(a) Give the equation for total revenue for x units per year. (b) Give the equation for total costs for x units per year. (c) What is the “breakeven” level of x? (d) If you sell 1500 units this year, will you have a profit or loss? How much? (e) At 1500 units, what are your marginal and average costs?
- Calculate the value of total revenue if total cost is $6500 and profits are $800Cost, revenue, and profit are in dollars and x is the number of units. Suppose that the marginal revenue for a product is MR = 1800 and the marginal cost is MC = 90Vx + 4, with a fixed cost of $600. (a) Find the profit or loss from the production and sale of 5 units. There is a -Select-- | of $ (b) How many units will result in a maximum profit? unitsIf explicit cost equals to $40000 and implicit cost $ 95,000 and the accounting profit is $23,000 what is the revenue and the economic profit