A firm produced two types of television x of type A and y of type B per year (in thousands). If the revenue and cost equations for the year are (in million dollars) R(x, y) = 3x+6y C(x, y) = x2 + y2-3x-2y-8 Determine how many of each type of television should be produced per year to maximize profit? What is the maximum profit?
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- 6. Let p(x) = 4 – 0.0002x be the price (in TL) of each unit of a certain product required to attract a demand of x units in a year and let C(x) = 600 + 3x be the total cost of producing x units of the product in a year. (a) (- as large as possible? What is the number of units that should be produced to make the yearly profit (b) What is the yearly profit in case (a)The following graph illustrates the weekly demand curve for motorized scooters in Madison. Use the green rectangle (triangle symbols) to compute total revenue at various prices along the demand curve. Note: You will not be graded on any changes made to this graph. PRICE (Dollars per scooter) 325 300 275 250 225 200 175 150 125 100 75 50 25 0 0 10 A + 20 30 X B Demand 40 50 60 70 80 QUANTITY (Scooters) 90 100 110 120 130 Total Revenue ?8. (a) At a health food manufacturing plant, it costs $20000 to produce 1500 cases of tofu, and $26000 to produce 2000 cases of tofu. Find this manufacturer's linear cost function based on this information. (Let r be the number of cases of tofu.) (b) Each case of tofu is then sold for $18. Find this manufacturer's revenue function. (c) Find this manufacturer's profit function and simplify it. (d) What is the break-even point for this business?
- Cost (thousands of $) The graph shown on the right represents the cost C (in thousands of dollars) of refining x gallons of gasoline per hour (in thousands). The vertical axis represents the cost, and the horizontal axis represents the number of gallons of gasoline refined. Cost of refining gasoline per hour 1000- 800- 600- 400- Answer the following questions below in parts (a) through (d). 200 O 100 200 300 400 500 600 700 800 Number of Gallorns (thousands) (a) What is the cost of refining 200 thousand gallons of gasoline per hour? thousandfunction 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:5. The profit, P(x), of a video company, in thousands of dollars, is given by the equation P(x) = -5x + 550x -5000, where x is the amount spent on advertising, in thousands of dollars. Determine the least amount spent on advertising that will result in a profit of at least $4 000 000.
- 2. What is the relationship between the total cost curve, and the average cost per unit? Explain their relationship, and draw a diagram showing how the two are related. The total cost of production, in thousands of dollars, is C(q) = q³ 12q² + 60q, where q is in thousands and 0 ≤ q ≤ 8. (a) Graph C(q). Estimate visually the quantity at which average cost is minimized. (b) Determine analytically the exact value of q at which average cost is minimized.Crawford Computing finds that its weekly profit, in dollars, from its production and sale of x laptop computers is P(x)=-.002x^3-.15x^2+400x-800 Currently, Crawford builds and sells 9 laptops weekly. (a) what is the current weekly profit? (b) how much profit would be lost if production and sales dropped to 8 laptops weekly? (c) what is the marginal profit with x=9? (d) use answers from parts (a) and (c) to estimate the profit resulting from the production and sale of 10 laptops weekly.It costs a baker a fixed cost of $420 and variable cost of $2.10 per cupcake. A cupcake is sold for $4.90 each. (iv) Write an algebraic expression representing the revenue R as a function of the number of cupcakes x sold.(v) Graph both functions on the same coordinate axes.(vi) From your graph find coordinatae at which cost equals revenue.(vii) Using your graph, determine how many cupcakes need to be made to produce revenue of at least $1,029. How much profit is made for this number of cupcakes?
- 5. In an FEA simulation, you did a mesh independence study. The results were compared with an experimental test and errors were plotted in Figure 7. a) Is the mesh with 8000 elements fine enough, and why? b) Is there another error source in the simulation and what type of errors could it be? Page 3 of 6 ENGG20071 Industrial Design & Product Case Studies Errors 60% 50% 40% 30% 20% 10% 0% 500 1000 2000 4000 8000 Figure 7 Errors plot against number of elementsQ 0 1 3 5 7 9 11 15 17 Total Cost (TC) 1350 3200 4800 6900 9100 12350 18650 Total Fixed Cost (TFC) Total Variable Cost (TVC) 500 Average Total Cost (AC) 700 2. Plot the TC, TFC and TVC curves on a single diagram on another. cost of mountain bike production. Average Variable Cost (AVC) Average Fixed Cost (AFC) 200 220 Marginal Cost (MC) and plot the AC, AFC, AVC and MC curvesork (5.3) Part 1 of 3 A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The relevant manufacturing data are given in the table. Labor Hours per Ski Maximum Labor-Hours Available per Day 120 25 Department Fabricating Finishing Answer parts (A), (B), and (C) below Trick Ski 5 1 Slalom Ski 4 1 CITT (A) If the profit on a trick ski is $50 and the profit on a slalom ski is $60, how many of each type of ski should be manufactured each day to realize a maximum profit? Wh is the maximum profit? The maximum profit is $ The maximum occurs when trick skis and slalom skis are produced. 4