1. ThedemandfunctionforagoodisgivenbytheequationP=a−bQwhilethetotal cost function is TC = dQ2 + eQ + f, where a, b, d, e and f are positive constants. (a) Derive the equation for profit. (b) Derive an expression for the value of Q for which profit is
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1. ThedemandfunctionforagoodisgivenbytheequationP=a−bQwhilethetotal
cost function is TC = dQ2 + eQ + f, where a, b, d, e and f are positive constants. (a) Derive the equation for profit.
(b) Derive an expression for the value of Q for which profit is maximised.
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- 2AAWO AC I4 17.1 REVENUE, COST, AND PROFIT APPLICATIONSITSO RSYHAHD 797 20 A firm sells each unit of a product for $50. The total cost of producing x (thousand) units is described by the function C(x) = 10 – 2.5x² + x³ where C(x) is measured in thousands of dollars. (a) Use the marginal approach to determine the profit-maximizing level of output. (6) What is total revenue at this level of output? Total cost? Total profit? 1 The profit function for a firm is -000Please assist with the last question. Thank you.Define the term autartky. What is its pro and con.
- Profit Suppose that the total weekly cost for theproduction and sale of x bicycles is C(x) = 23x +3420 dollars and that the total revenue is givenby R(x) = 89x dollars, where x is the number ofbicycles.a. Write the equation of the function that models theweekly profit from the production and sale of xbicycles.b. What is the profit on the production and sale of150 bicycles?c. Write the function that gives the average profit perbicycle.d. What is the average profit per bicycle if 150 areproduced and sold?A toy manufacturer makes miniature trucks. The pricep(in dollar) and the demandx(numberof miniature trucks) are related by the equation 6000−600p=x. The total cost for the sametoy manufacturer to producexminiature trucks can be modeled byC(x) = 8x+ 450.(a) (10 points) Express the pricepin terms of the demandx. Find the revenueR(x) if themanufacturer sellsxminiature trucks in a month and find the domain of this function.(b) (10 points) Graph the cost and revenue functions on the same coordinate system for 0≤x≤6000.(c) (10 points) What is the minimum number of trucks the toy manufacturer must sell tobreak even?(d) (10 points) FindP′(300) and interpret the result.(e) (10 points) What is the exact profit from the sale of the 301stminiature truck?Problem 1 (a) TeddyJ is a manufacturer of dish washing liquid. If his monthly demand function for 750ml Size is q = 4000 - 250p and his total cost function is C(q) = 500+0.2q. %3D %3D (i) Derive an expression, R(g) for Teddy J's total revenue curve. (11) Derive an expression, I(q) for Teddy J's profit function. (iii) Determine whether Teddy J's profit is increasing or decreasing when he produces 5 hundred, 750ml bottles of dish washing liquid.
- 920 it bait of 289301 Sindspis ON SEU pilkupeni A30S AO +32 monulo2 An economist for a sporting goods company estimates the revenue and Cost functions for the production of a new snowboard. These Functions are R(x) = -x ² +10x and ((x) = 4x+5, respectively, where x is the number of Snowboard's produced in thousands. The average profit is defined by the function AP(x) = P(x), where pox) is the profit function & Determine the production levels that make AP(x) > 0 P-xdfunction 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:Refer to the diagramhe ight. The vtal diterence beween curves Fand G measures OA fxed costs O B. marginal costs OC. average fred costs O D. sunk costs. Quantily of oulpul