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A farmer uses K units of machinery and L hours of labor to produce C tons of corn, with the production function, C= 2L0.5 K. The farmer currently uses L = 20 and K = 10. Suppose the input price ratio is w/r = 1. What would you tell the farmer to do in order to minimize his cost of production given the current level of output?
a. You should use more machinery and more labor.
b. You should use more machinery and less labor.
c. You should use less machinery and more labor.
d. You should use less machinery and less labor.
Suppose that a latte can only be produced by using exactly 1 ounce of espresso (E) and 3 ounces of milk (M). What is the firm's cost function if the price of espresso is 0.50 per ounce and the price of milk is 0.10 per ounce?
a. C = 4q
b. C = 0.8q
c. C = 0.4q
d. C = 160q
e. C = 80q
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- A company produces and sells luxury goods and is able to control the demand for the product by varying the selling price. The relationship between price and demand is found to be p = 10 − 42 D2 + 2D where p is the price per unit in million dollars and D is the demand per year. The company is seeking to maximize its profit. The fixed cost is $59 million per year and the variable cost is $25 million per unit. The production capacity is 42 units per year, and the company produces at least 1 unit per month. a) Derive how to find the number of units that should be produced annually to maximize profit. b) What is the maximum profit per year? c) What is the annual breakeven point? d) What is the company’s range of profitable output per year?A company manufactures two products. If it charges aprice pi for product i, it can sell qi units of product i, whereq1 60 3p1 p2 and q2 80 2p2 p1. It costs $25to produce a unit of product 1 and $72 to produce a unit ofproduct 2. How many units of each product should beproduced to maximize profits?AutoTime, a manufacturer of electronic digital timers, has a monthly fixed cost of $50,000 and a production cost of $7 for each timer manufactured. The timers sell for $15 each. (a) What is the cost function C(x)?C(x) = (b) What is the revenue function R(x)?R(x) = (c) What is the profit function P(x)?P(x) = (d) Compute the profit (loss) corresponding to production levels of 3000, 6000, and 11,000 timers, respectively. (Input a negative value to indicate a loss.) 3000 timers $ 6000 timers $ 11,000 timers $
- An analyst is constructing a simple model to determine the gross and net profit of a product, given its profit per unit, quantity sold, and the total costs assigned to the product. The calculation for gross profit is Profit per Unit times Quantity. The calculation for Net Profit is Gross Profit minus Total Costs. A B 1 2 Profit per Unit 2 3 Quantity 19,400 4 Gross Profit 5 6 Total Costs 9,600 7 8 Net Profit With the values for Profit per Unit, Quantity, and Total Costs shown above, what should the model return for the following calculated cellsAssume the demand for a company’s drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year,it will cost $16x. Each unit of Wozac is soldfor $3. Each unit of Wozac produced -incurs a variable production cost of $0.20. It costs $0.40 per year to operate a unit of capacity.Determine how large a Wozac plant the company should build to maximize its-expected profit over the next 10 years.Consider a monopolistically competitive market with NN firms. Each firm's business opportunities are described by the following equations: Demand: Q=100N−PQ=100N−P Marginal Revenue: MR=100N−2QMR=100N−2Q Total Cost: TC=50+Q2TC=50+Q2 Marginal Cost: MC=2QMC=2Q How much profit does each firm make? a: 1,250/N*2−50 b: 2,500/N*2−50 c: 50+625/N*2 d: 1,875/N*2 In the long run, how many firms will exist in this market?
- A handicraft products trader is selling leather cases for $40 the unit. To run his business, he needs to pay $10000 for rent, $5000 salaries, and another $5000 for marketing campaigns. The handicraft trader has the choice to import his products from different countries, and it will cost him $20 per unit if the product comes from China, $25 per unit if the product comes from India, and $15 per unit if the product comes from Malaysia. Questions: 1. If the trader must choose to import his products from one country, then which country will it be? 2. compute the trader’s profit if he sells 40 units imported from China and 50 units imported from India. 3. compute the trader’s profit if he imports only from China and sells 500 then 2000 units. Explain the obtained results. 4. What is the trader total cost from importing 100 units from Malaysia and 200 units from India ? 5. If the trader decides to import only from China, how many units he should sell to reach a profit of $2000? 6. If…A manager wants to know how many units of each product to produce on a daily basis in order toachieve the highest contribution to profit. Production requirements for the products are shown inthe following table.ProductMaterial 1(pounds)Material 2(pounds)Labor(hours)A 2 3 3.2B 1 5 1.5C 6 — 2.0Material 1 costs $5 a pound, material 2 costs $4 a pound, and labor costs $10 an hour. Product Asells for $80 a unit, product B sells for $90 a unit, and product C sells for $70 a unit. Availableresources each day are 200 pounds of material 1; 300 pounds of material 2; and 150 hours of labor.The manager must satisfy certain output requirements: The output of product A should not bemore than one-third of the total number of units produced; the ratio of units of product A to units ofproduct B should be 3 to 2; and there is a standing order for 5 units of product A each day. Formulate a linear programming model for this problem, and then solveA company manufactures two products. If it chargesprice pi for product i, it can sell qi units of product i,where q1 = 60 - 3p1 + p2 and q2 = 80 - 2p2 + p1. Itcosts $5 to produce a unit of product 1 and $12 to produce a unit of product 2. How many units of eachproduct should the company produce, and what pricesshould it charge, to maximize its profit? Use spreadsheet modelling in Excel
- (1) When chef Paolo prices his speciality ‘pizza-n-all’ meal at £25, he sells 20 meals a day. When he prices his pizza meal at £22, he sells 21 meals a day. Suppose Paolo reduces his price from £25 to £22. Explain the impact of the price reduction on the revenue he receives from the first 20 meals he sells. Total Revenue – Price X Quantity. Revenue @ £25 = £25 X 20 = £500. Revenue @ £22 = £25 X 20 = £440 The impact of the price reduction is a reduction in total revenue of £60 (-12%) over the first 20 meals that he sells. Calculate the additional revenue generated from the additional meals he sells when he lowers his price to £22. Total Revenue = Price X Quantity. Total Revenue @ £22 = £22 X 21 = £462. Additional Revenue = Revenue @ £25 – revenue @ £22 = £500 - £462 = -£38. Calculate the marginal revenue Paolo receives from the 21st meal. How does that amount relate to the amounts you calculated in (a) and (b)? (3%) Suppose Paolo reduces his price from £25 to £22. Explain…The fixed costs of Chun Company are $309,000 and the total variable costs for its only product are 45% of the sales price, which is $100. Chun currently sells 7,400 units per month and is looking to sell more. Consider each of the following independently: Part A The marketing manager is considering lowering base salaries of salespeople by a collective amount of $39,000 per month while increasing the sales commission by $8 per unit. He believes this will increase monthly sales by 130 units. If so, what would the effect of this change in compensation have on monthly income? INCREASE OR DECREASE of $BLANK Part B Management believes monthly sales can be increased by 570 units if additional quality control steps are taken. These steps would mean an increased variable cost per unit of $10. What is the expected effect on the company's monthly income of adding these additional quality control steps? (DECREASE OF 48,350, DECREASE OF 54050, DECREASE OF 48892, OR INCREASE BY 25650)1. Cox Electric makes electronic components and has estimated the following for a new design of one of its products. Fixed cost = $24,375 Material cost per unit = $0.17 Labor cost per unit = $0.12 Revenue per unit = $0.68 Note that fixed cost is incurred regardless of the amount produced. Per-unit material and labor cost together make up the variable cost per unit. Assuming that Cox Electric sells all that it produces, profit is calculated by subtracting the fixed cost and total variable cost from total revenue. Construct an appropriate spreadsheet model to find the profit based on a given production level and use the spreadsheet model to answer these questions. a. Construct a one-way data table with production volume as the column input and profit as the output. Breakeven occurs when profit goes from a negative to a positive value; that is, breakeven is when total revenue = the total cost, yielding a profit of zero. Vary production volume from 0 to 100,000 in increments of 10,000.…