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- 6) When the toll for a bridge crossing increased from $2 to $2.50; the daily volume decreased from 30,000 to 26250 vehicles per day. Determine the optimum toll and the maximum daily revenue.Answer the given problem.1. Annie bought one dozen smartphones for P200,000.00 with a discount of 5%. She sold half dozen at a price of P18,000.00 per unit. However, a new model of smartphone became available in the market, so she sold the remaining half dozen @ P12,000.00 each unit. What was her profit or loss?Please show solution for this question. Determine the revenue (R) and cost (TC). The production will vary according to the sales volume. Express the equation as follows. R = 100N – 0.001N2 TC = 0.005N2+4N+60,000 Find 1) The most profitable production volume. 2) Volume of production at break even point. 3) Production volume with lowest average cost. Answer 1) 8,000 units 2) 6,000 units 3) 3,464 units
- A seller can sell 3 diamond rings at a price of $12000 each. If he sells 4, his MR will be $10500. what is total revenue?Suppose we know that p=1,056- D/5, where p = price in dollars and D = annual demand. The total cost per year can be approximated by $1,000+ 2D2. a.Determine the value of D that maximizes profit. b.Show that in part(a) profit has been maximized rather than minimized. c. Find the maximum profit Show complete solution.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?
- Suppose we know that p=1,056– D/5, where p = price in dollars and D = annual demand. The total cost per year can be approximated by $1,000 + 2D2 . a.Determine the value of D that maximizes profit. b.Show that in part(a) profit has been maximized rather than minimized. c. Find the maximum profit. The cost of a window air conditioner was $350. During a spring promotion, the selling price was reduced by $150. The required overhead expenses and operating profit for the air conditioner are 25% and 15% of selling price respectively. a) What is the regular selling price? b) What is the break-even price? c) What is the profit (loss) at the sale price? 3. Frigid Boards purchases one of its snowboards for $395 less a retail trade discount of 15% and a loyalty discount of 4%. Its markup on selling price percentage on all snowboards is 21%. At the end of the season, any leftover snowboards are marked down by 10%. What is the sale price of snowboard?The durax tire company recaps tires. The weekly fixed cost is $2500 and the variable cost per tire is $9. Price is related to demand, according to the following linear equation: V = 200 - 4.75p Develop the nonlinear profit function for the tire company and determine the optimal price, the optimal value, and the maximum profit per week.
- A 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…For the toatl revenue equation R(q)=1000+1000q-8q^2 how does the second order sufficient condition establish that there is a maximum total revenue? What is the quantity where total revenue is maximized?A recent engineering was given the job of determining the best production rate for a new type of casting in a foundry. After experimenting with many combinations of hourly production rates and total production cost per hour, he summarized his findings in (table 1). The engineering then talked to the firm’s marketing specialist, who provided estimates of selling price per casting as a function of production output (see table 2). There are 8,760 hours in a year. What production rate would you recommend to maximize total profits per year? Table 1 Total cost per hr Casting production per hr $1,000 100 $2,600 200 $3,200 300 $3,900 400 $4,700 500 Table 2 Selling price / casting Casting production per hr $20.00 100 $17.00 200 $16.00…