6. [-/2 Points] TANAPCALC10 2.6.034. Cost of Producing Surfboards The total cost C(x) (in dollars) incurred by Aloha Company in manufacturing x surfboards a day is given by the following function. C(x) = 14x2 + 500x + 150 where (0 S x S 15) (a) Find C'(x). C'(x) = (b) What is the rate of change of the total cost (in dollars) when the level of production is 6 surfboards a day? $ per surfboard Need Help? 7. [-/3 Points] TANAPCALC10 2.6.036. Demand for Tents The demand for Sportsman 5 x 7 tents is given by the following function where p is measured in dollars and x is measured in units of a thousand. (Round your answers to three decimal places.) p = f(x) = o.1x2 x+ 40 (a) Find the average late of change in the unit price of a tent if the quantity demanded is between the following intervals. between 4700 and 4750 tents $ per 1000 tents between 4700 and 4710 tents $ per 1000 tents (b) What is the rate of change of the unit price if the quantity demanded is 4700? $ per 1000 tents 8. [-l5 Points] (a) Find the revenue function R. R(x) = (b) Find the marginal revenue function R'(x). R'(X) = (c) Compute the following value. R'(7,400) = Interpret your results. When the level of production is NeeaHem TANAPCALC1 D 3.4.010. p = -0.03x + 350 (0 s x 5 20,000) units, the production of the next speaker system will bring an additional revenue of 9. [I2 Points] DETAILS TANAPCALC1D 3.4.012. Marginal Revenue for an Apartment Complex Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting x apartments is represented by the following function. P(x) = -9x2 + 1820x - 47000 (a) what is the actual prot realized from renting the 415t unit, assuming that 40 units have already been rented? s (b) Compute the marginal prot when x = 40 and compare your results with that obtained in part (a). $ dollars. MY NOTES PRACTICE ANOTH Marglnal Revenue for Produclng Loudspeakers The management of Acrosonic plans to market the EIectroStat, an electrostatic speaker system. The marketing department has determined that the demand for these speakers is represented by the following function, where 9 denotes the speaker's unit price (in dollars) and x denotes the quantity demanded. Find the following functions (in dollars), find the value (in dollars) and interpret your results. PRACTICE ANOTH 10. [-I3 Points] TANAPCALC10 2.R.062. Manufacturing Costs Suppose that the total cost of manufacturing x units of a certain product is C(x) dollars. (a) What does C'(X) measure? Give units. 0 The instantaneous rate of change of the number of producls produced x (in units) when c dollars are spent. 0 The instantaneous rate of change of the total manufacturing cost c in dollars when x units of a certain product are produced. 0 The average rate of change of the total manufacturing cost c in dollars when x units ofa certain product are produced. 0 The average rate of change of the number of products produced x (in units) when c dollars are spent. (b) What can you say about the sign of C'? O The sign is always positive. 0 The sign is always negative. 0 C' is always zero. 0 Not enough information is given to determine the sign of C'. (c) Given that C'(1800) = 15, estimate the additional cost (in dollars) to be incurred by the company in producing the 1,8015t unit of the product. (Round your answer to the nearest dollar.)