Your firm's research department has estimated your total revenues to be R left parenthesis Q right parenthesis equals 30 comma 000 Q minus 80 Q squared and your total costs to be C left parenthesis Q right parenthesis equals 1 comma 000 plus 20 Q squared. What level of Q maximizes net benefits?
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- You are the manager of a firm that specializes in small single-board widgets. Your goal is to determine the number of units (Z) that must be produced and sold by your firm each month in order to maximize profits. The total benefits (revenues) and costs to your firm of producing various quantities are given in the first three columns of the following table. Based on this scenario, complete the table and answer the accompanying questions: Control Variable Z Total Benefits B(Z) Total Cost C(Z)0 0 01 200 102 380 303 540 604 680 1005 800 1506 900 2107 980 2808…Revenue from product X is $11,000, variable costs are $7,000, and allocated fixed costs are $6,000. If you drop product X in the long term, profit will:Each coffee table produced by Kevin Watson Designer nets the firm a profit of $9. Each book case yields a $12 Profit. Watson's fim is small and it resources limited. During any given production period ( of 1 week ),10 gallons of varnish and 12 lenght of high-quality redwood are available. Each coffee table requires approximately 1 gallon of varnish and 1 lenght of redwood. Each bookcase takes 1 gallon of varnish and 2 lenghts of wood. if the profit for the coffee table is increased from $ 9 to $ 15, what is the new optimal solution? (also, you should show the process of how to get new optimal solution)
- TRUE OR false.. The firm should shut down its operations if the total revenue cannot cover the total variable costYou cannot equate coffee roaster explicit costs with coffee farmers’ explicit benefits, despite coffee roasters paying the farmers for their beans. What are some of the factors that account for this discrepancy? Why does the roaster care about the profitability of the coffee farmer? Why would they offset their reduced production costs by increasing the amount they pay to farmers?Average and marginal profit Let C(x) represent the cost ofproducing x items and p(x) be the sale price per item if x items aresold. The profit P(x) of selling x items is P(x) = xp(x) - C(x)(revenue minus costs). The average profit per item when x items aresold is P(x)/x and the marginal profit is dP/dx. The marginal profitapproximates the profit obtained by selling one more item, given that x items have already been sold. Consider the following cost functions Cand price functions p.a. Find the profit function P.b. Find the average profit function and the marginal profit function.c. Find the average profit and the marginal profit if x = a units are sold.d. Interpret the meaning of the values obtained in part (c). C(x) = -0.02x2 + 50x + 100, p(x) = 100 - 0.1x, a = 500
- Your software company recently instituted a highly regarded training program for newly hired software developers. The benefits of this program include not only the benefits to employees, but also the goodwill generated by an increase in your reputation among customers and professional groups. The costs of this training program include all of the labor, space, and consultants necessary. Suppose these benefits and costs are given by B(Q) = 100Q − 2Q2 and C(Q) = 10Q, where Q represents the amount of hours each software developer should spend in training. (Note that MB = 100 − 4Q, MC = 10, and also that time can be measured in fractions of one hour.) a. What level of Q maximizes the total benefits of your newly introduced training program?b. What level of Q minimizes the total costs of the program?c. What level of Q maximizes the net benefits?d. What level of training is optimal? Why?PLEASE ANSWER D Your software company recently instituted a highly regarded training program for newly hired software developers. The benefits of this program include not only the benefits to employees, but also the goodwill generated by an increase in your reputationamong customers and professional groups. The costs of this training program include all of the labor, space, and consultants necessary. Suppose these benefits and costs are given by B(Q) = 100Q − 2Q2 and C(Q) = 10Q, where Q represents the amount of hours each software developer should spend in training. (Note that MB = 100 − 4Q, MC = 10, and also that time can be measured in fractions of one hour.) a. What level of Q maximizes the total benefits of your newly introduced training program?b. What level of Q minimizes the total costs of the program?c. What level of Q maximizes the net benefits?d. What level of training is optimal? Why?You manage a large retail supercenter that sells groceries and other products to 30,000 customers per week. Currently, you employ 80 check-out clerks and 10 automated check-out machines (customers scan and pay for their purchases without a clerk's assistance). Each clerk is paid wages and fringe benefits of 800 dollars per week. It also cost you 800 dollars per week to lease each machine (price includes installation, software support and servicing). A vendor has offered you to lease you additional machines at this price. You estimate that by leasing 10 more machines you can meet your service requirements with 30 fewer clerks. Should you lease the additional machines or continue to service your customers with your current input mix? You conduct additional analysis and estimate that you can service the 30,000 customers with the following combinations of clerks and machines. Calculate the total costs for each of these combinations. What combination of inputs serves the customer at the…
- A manufacturer has found out that if he is to increase his current sales, he must lower his current price. His marginal revenue (MR) from an output x is given by the expression MR=148 – 2x. The marginal production cost (MC) is Ksh 36 and fixed costs amount to Ksh 1,000. Required i) Derive the revenue and total cost functions. ii) Determine the output and price that would maximize profit. iii) Compute the maximum profit.A restaurant frequently offers a special prix fixe meal and has been charging $120 per person for the event. At that price, they’ve been averaging 40 customers each time. Their marketing firm has convinced them that they’ll gain a customer for every dollar they lower the cost of the event, and conversely lose a customer for every dollar they raise the cost. Their fixed cost per event is $$1200 and preparing each customer’s meal costs an additional $30. What are the break-even points in terms of customers served? Write the exact answer. Do not round. Separate multiple answers with a comma.Your software company recently instituted a highly regarded training program for newly hired software developers. The benefits of this program include not only the benefits to employees, but also the goodwill generated by an increase in your reputation among customers and professional groups. The costs of this training program include all of the labor, space, and consultants necessary. Suppose these benefits and costs are givenby B(Q) = 100Q − 2Q2 and C(Q) = 10Q, where Q represents the amount of hours each software developer should spend in training. (Note that MB = 100 − 4Q, MC = 10, and also that time can be measured in fractions of one hour.) a. What level of Q maximizes the total benefits of your newly introduced training program?b. What level of Q minimizes the total costs of the program?c. What level of Q maximizes the net benefits?