(b) A firm manufactures benches and tables: the quantity of benches manufactured is B and the quantity of tables manufactured is T. The total cost of manufacturing benches and tables is given by the equation: Cost = 3B2 + 5T² – 2BT. There is a shortage of lumber available to manufacture these items, and so, only 60 items in total have been promised to a customer. (i) Create the Lagrangian expression for Cost. (ii) The Lagrangian equations are given: 6B – 2T – 1 = 0 10T – 2B – 1 = 0 60 – B -T= 0 Calculate the minimum cost possible. (iii) If more lumber now becomes available, what selling price would be required to make a profit on an additional item produced?
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- Suppose that the dollar cost of producing x appliances is c(x) = 1000 + 70x-0.1x². a. Find the average cost per appliance of producing the first 100 appliances. b. Find the marginal cost when 100 appliances are produced. c. Show that the marginal cost when 100 appliances are produced is approximately the cost of producing one more appliance after the first 100 have been made, by calculating the latter cost directly. CUCKO The average cost per appliance of producing the first 100 appliances is $ (Round to the nearest cent as needed.) /appliance.Suppose the total cost of producing T-shirt can be TC = 50+2q. The average cost of 5th T-shirt?The cost of renting tuxes for the Choral Society's formal is $21 down, plus $87 per tux. Express the cost C as a function of x, the number of tuxedos rented. C(x) = Use your function to answer the following questions. (a) What is the cost of renting two tuxes? %$4 (b) What is the cost of the second tux? $4 (c) What is the cost of the 4,098th tux? 2$ (d) What is the variable cost? %24 What is the fixed cost? $4 What is the marginal cost? %24
- The variable x represents the number of HDTVs manufactured and sold in a given month. The variable p is the price charged when you sell a TV. A demand curve is given by p = 660-3x. a) Find the x-intercept of this demand curve. Say what it means. Assume you must pay salaries totalling 8000$ in a month. Also, it costs $110 to manufacture one TV. b) Write a formula for your cost function C(x) c) Write a formula for your revenue function R(x) d) The profit function is M(x) = Graph the profit function and using the Maximum program, find the maximum possible profit and fill in the details (round off x to the nearest whole number): e) number of sales: f) profit: g) selling price: h) revenue: i) cost: j) check these results fit together: k) Find the range of prices you can charge and still be in the black: The lowest price you can charge is ___________ and the highest is ___________The cost, in thousands of dollars, of airing x television commercials during a sports event is given by C(x) = 150 + 2,600x – 0.06x2. (a) Find the marginal cost function C'(x). C'(x) = (b) Use the marginal cost to approximate the cost to air the 5th commercial. Convert your answer to dollars. The cost to air the 5th commercial is approximately X dollars. (c) What is the exact cost to air the 5th commercial? Convert your answer to dollars. The exact cost to air the 5th commercial is x dollars.Cost, Revenue & ProfitFor these problems, xx will represent the number of items and yy will represent the money.The fixed costs for a certain item are $215 per week. The cost to produce each item is $2 per item.Using this information, what is the cost equation? Give your answer in slope-intercept form:y=y= The retailer intends to sell each item for $13/item.Using this information, what is the revenue equation? Give your answer in slope-intercept form:y=y= If in this week 13 items are made, and all items are sold in the week, what are the total costs to the retailer?Cost = $What is the revenue from selling 13 items?Revenue = $Finally, what is the profit for this retailer?Profit = $Box 1 & 2: Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/cBe sure your variables match those in the question.
- function for the lightweight compasses is given by p = 40- 4q²where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (i) Write an equation giving profit as a function of the number of lightweight compasses produced. (ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit? Type your answer here:To produce the next popular toy, a company has to pay a factory $250, 000 to set up the production line. They also have to pay $25 per item for the raw materials and labor. Write function for the average cost to produce x items. Then describe what happens to the average cost as the factory produces a large number of toys.A certain electronics manufacturer found that the cost C to produce x DVD/Blu-ray players can be found using the 0.04x? + 8x + 800. If the marginal cost equation C were $19.2, how many DVD/Blu-ray players were produced?
- Ten-year old Sarah is starting a lemonade stand, she uses baskets of lemons (L) and other ingredients (O). She is able to produce lemonade according to the production function f(L, O) = 1 2 L 2O. The cost of a basket of lemons is $10 and the average cost of the other goods is $4. (a) Derive MPL and MPO. (b) Currently Sarah is using 4 baskets of lemons and 40 units of the other goods. Using this information, calculate MPL and MPO. (c) True/False. At her current use of inputs Sarah is minimizing costs. If true, explain why. If false, what would you recommend Sarah do? (d) Sarah wants to produce 320 units of lemonade. Determine the cost minimizing combination of inputs to use. (e) Assuming no changes in the market price of lemonade nor in the prices of the inputs, if Sarah continues to produce 320 units of lemonade in the long run, what will Sarah’s long run costs be.The marginal cost of producing the xth box of light bulbs is 4 + x2 dollars per box. Determine how much is added to the total cost by a change in production from x = 20 to x = 80 boxes. 1,0001/3 1/3 Farmer Joe's production function is f(x1, x2) = ", where xị is the number of pounds of lemons he uses and x2 is the number of hours he spends 1/21/2 2wi"wy3/2, where y is the squeezing them. His cost function is c(w1. w2, y) = number of units of lemonade produced. (a) If lemons cost $1 per pound, the wage rate is $1 per hour, and the price of lemonade is p, what is his marginal cost function?