1. Given the price-demand function p(x)=-4x+320, and Total cost function C(x)=40x+3604. (a) Using Break-even analysis, state the range of values that guarantees profit. (b) Find the unit price that yields maximum profit.
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- Q1. Game console manufacturing determines that in order to sell Q units, the price per unit (in dollar) must decreased by the linear demand (the demand function) P(Q)= 800- 0.3Q($/device) The manufacturer also determine that the cost depends on the volume of production and includes a fixed part 500,000($) and a variable part 500Q , that is C(Q)= 500000+ 500Q What price per unit must be charged to get the maximum profit?The Hickory Cabinet and Furniture Company makes chairs. The fixed cost per month of making chairs is $7,500, and the variable cost per chair is $40. Price is related to demand, according to the following linear equation: v = 400 - 1.2p Develop the nonlinear profit function for this company and determine the price that will maximize profit, the optimal volume, and the maximum profit per month.Which of the ff statements are true about cost function a. It estimate the total cost of production given a specific budget b. It helps predict what the marginal cost would be to produce a product at different levels of output c. It allows management to evaluate how efficiently the production process was at the beginning of the operation period d. It helps manager understand the price behavior of the product A firm profit maximization point is where a. Total revenue Is greater than total cost b. Marginal revenue is equal to marginal cost c. Marginal revenue is greater than total cost d. Marginal cost is less than total cost
- Suppose a company has fixed costs of $1500 and variable costs of (3/4)x + 1120 dollars per unit, where x is the total number of units produced. Suppose further that the selling price of its product is 1200 − (1/4)x dollars per unit. (a) Find the break-even points. (Enter your answers as a comma-separated list.)x = (b) Find the maximum revenue. (Round your answer to the nearest cent)$ (c) Form the profit function, P(x), from the cost and revenue functions.P(x) = Find maximum profit. (Round your answer to the nearest cent.)$ (d) What price will maximize the profit? (Round your answer to the nearest cent.)Suppose a company has fixed costs of $300 and variable costs of 3/4 x+1460 dollars per unit, where x is thetotal number of units produced. Suppose further that the selling price of its product is 1500−1/4 x dollars per unit.(a) Find the break-even points.(b) Find the maximum revenue.(c) Form the profit function from the cost and revenue functions and find maximum profit.(d) What price will maximize the profit?the mahogany cabinet and furniture company makes chairs. the fixed coat per month of making chairs is $7500 and the variable cost per chair is $40. price is related to demand, according to the following linear equation: v = 400 - 1.2p develop the nonlinear profit function for this company and determine the price that will maximize profit, the optimal volume, and the maximum profit per month
- Suppose a company has fixed costs of $53,200 and variable cost per unit of 1/3x + 444 dollars, where x is the total number of units produced. Suppose further that the selling price of its product is 2372 − 2/3x dollars per unit. (a) Find the break-even points. (Enter your answers as a comma-separated list.) x = (b) Find the maximum revenue. (Round your answer to the nearest cent.) $ (c) Form the profit function P(x) from the cost and revenue functions. P(x) = Find maximum profit. $ (d) What price will maximize the profit? (Round your answer to the nearest cent.) $Thranduil company’s market research department is working on the pricing of a product. The field research shows that average demand is expected to be 8000 units at price 50 TL. From this point, each 1 TL change in price will negatively affect demand with a magnitude of 100 units. Fixed and variable costs are confronted for producing the product. According to the information obtained from the financial department, 200,000 TL is the estimate of fixed costs and 20 TL is the estimate of variable costs per unit produced. Assume that all units produced are sold.Which of the following prices is the one that maximizes the company's profit?(show complete solution, formula and explanation) A company produces and sells a consumer product and thus far has been able to control the volume of the product by varying the selling price. The company is seeking to maximize its net profit. It has been concluded that the relationship between price and demand, per month, is approximately D = 500 – 5p, where p is the price per unit in dollars. The fixed cost is $1,000 per month, and the variable cost is $20 per unit. Obtain the answer mathematically to the following questions: a.What is the optimal number of units that should be produced and sold per month? b.What is the maximum profit per month? c.What are the breakeven sales quantities and the range of profitable demand volume?
- For April 2021, the actual cost per ASM (available seat mile) for Southwest Airlines was approximately 12.30. This as our best estimate of marginal cost, and assuming the price elasticity of demand is -3.5, find the profit maximizing air fare for Southwest Airline?A company estimates that the relationship between. unit price and demand per month for a potential new product is approximated by p= $100.00-$0.10D. The company can produce the product by increasing fixed costs $17,500 per month, and the estimated variable cost is $40.00 per unit. What is the demand that maximizes revenue and the maximum revenue? What is the optimal demand, D*, and based on this demand, should the company produce the new product? Why? (Work out the complete solution by differential calculus, starting with the formula for profit or loss per month.)Business Unit A, the supplying business unit, is selling to an outside market. It has excess capacity and can use it to transfer product to the receiving business unit, Business Unit B. Business Unit A does not incur incremental fixed costs in the production of the units supplied to Business Unit B. The formula to calculate the transfer price in this scenario is:? a. (Total variable costs + incremental fixed cost) ÷ total units supplied b. (Total variable costs + Contribution margin lost) ÷ total units supplied c. (Total variable costs + incremental fixed costs + Contribution margin lost) ÷ total units supplied d. Total variable costs ÷ total units supplied
