EXAMPLE 1.1 Alpha Associates has the following details: Fixed cost = Rs. 20,00,000 Variable cost per unit = Rs. 100 Selling price per unit = Rs. 200
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- Recall that profit equals revenue minus cost. For the revenue and cost functions shown, answer parts (a) through (e) below. R(x)equals=400x−2x^2 and C(x)equals=200x+4250, with 0≤x≤100 (a) Find the break-even point. The break-even point(s) is(are) x=?. (Type an integer or decimal rounded to one decimal place as needed. Use a comma to separate answers as needed.) (b) Find the x-value that makes profit a maximum. x=? (Type an integer or decimal rounded to one decimal place as needed.) (c) Find the maximum profit. The maximum profit is $? (Type an integer or decimal rounded to one decimal place as needed.) (d) For what x-values will a loss occur? Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to one decimal place as needed.) A. x<? or x>? B. x>? C. x<? D. ?<x<? (e) For what x-values will a profit occur? Select the correct choice below…Hilton Enterprises sells a product for $119 per unit. The variable cost is $68 per unit, while fixed costs are $436,968. Determine (a) the break-even point in sales units and (b) the break-even point if the selling price were increased to $124 per unit. a. Break-even point in sales units units b. Break-even point if the selling price were increased to $124 per unit unitsThe revenue and cost functions for a particular product are given below. The cost and revenue are given in dollars, and xrepresents the number of units . R(x) = −0.2x2 + 172x C(x) = 78x + 10065 (a) How many items must be sold to maximize the revenue?(b) What is the maximum revenue?
- Calculate the missing values. Express dollar values rounded to two decimal places and break-even volumes rounded up to the next integer. Fixed Cost (FC) per month Variable Cost (VC) Selling Price (5) per unit Total Variable Cost at Break- Revenue (TR) even (TVC) per month Break-even Total Volume (x) per month per month at Break-Even per unit $8,700.00 $24.00 $36.00 $0.00 $0.00 $130,000.00 $470.00 1,030 S0.00 $0.00 $0.00 $740.00 $79.00 22 $0.00 50.00 S0.00 $31.00 $53.00 440 S0.00 S0.00 S0.00 -1°CSuppose a company has fixed costs of $600 and variable costs per unit of x + 1130 dollars, where x is the total number of units produced. Suppose further that the selling price of its ²x product is 1200 - 1x dollars per unit. (a) Find the break-even points. (Enter your answers as a comma-separated list.) x = 10,60 (b) Find the maximum revenue. $ 2880000 (c) Form the profit function P(x) from the cost and revenue functions. P(x) = 1200x - 31²) - (600 + 1² +1130x) Find the maximum profit. $ 625 (d) What price will maximize the profit? (Round your answer to the nearest cent.) $ 35 XA cell phone company has a fixed cost of $1,000,000 per month and a variable cost of $22 per month per subscriber. The company charges $33 per month to its cell phone customers. a.What is the annual breakeven point for this company? b. The company currently has 95,000 subscribers and proposes to raise its monthly fees to $39.95, what is the new annual break-even point if the variable cost increases to $25 per customer per month? c.lf 20,000 subscribers will drop their services because of mönthly increase in part (b), will the company still be profitable?
- The Big Show drive-in has fixed costs of $ 6,916 per month and variable costs are $ 2.15 per ticket, if the owner decides to sell each of the ticket offices for $ 7.75 per person. 1. How many lockers must you sell per month to guarantee breakeven?A small company manufactures a certain product. Variable costs are $20 per unit and fixed costs are $10,875. The price demand relationship for this product is P = -0.25D + 250, where P is the unit sales price of the product and D is the annual demand. Total cost = fixed cost + Variable cost, TC = CF + CV Revenue = Demand x Price, TR = D x P Profit = Total Revenue – Total Cost, P = TR – TC a) Develop the equations for the total cost and total revenue. b) Find the breakeven quantity c) How many units must be sold to maximize profit? d) What is the company’s maximum profit?Ace Shoe Company sells heel replacement kits for men's shoes. It has fixed costs of $10 million and unit variable costs of $5 per pair. If the company charges $15 per pair, how many pairs must it sell to break even?
- A company manufactures and sells book-cases .The selling price is $54.90 per book case.The total cost.The total cost function is linear, and cost amounts to $50,000 for 2,000 book-cases and $32,120 for 800 book-cases. (a)Write the equation for revenue.(b)Write the equation for total cost. (c)Find the break even point.A division of a company produces income tax apps for smartphones. Each income tax app sells for $7. The monthly fixed costs incurred by the division are $20,000, and the variable cost of producing each income tax app is $2. (a) Find the break-even point for the division. (x, y) = (b) What should be the level of sales in order for the division to realize a 15% profit over the cost of making the income tax apps? (Round your answer up to the nearest whole number.)income tax appsA privately owned summer camp for youngsters has the following data for a 15- :weeksession Charge per camper $130 per week Fixed costs $42,000 per session Variable cost per camper $70 per week Сарacity 180 campers Develop the mathematical relationships for (a) .total cost and total revenue What is the total number of campers that (b) ?will allow the camp to just break even What is the profit or loss for the 12-week (c) ?session if the camp operates at 80% capacity