A lash adjuster keeps the pressure constant on engine valves, increasing automobile engines' fuel efficiency. The relationship between price (p) and monthly demand (D) for lash adjusters made by the Wicks Company is given by this equation: D=(2,000-p)/0.10. a) What is the demand (D) when total revenue is maximized? b) What important data are needed if maximum profit is desired?
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- 1. The cost function for a commodity is given by C(x) - 200+12x+0.1x² (S) and the demand funct is p-300-0.02x ($/unit) where x- quantity (demanded and produced). (a) What is the profit function for this commodity? (b) Find the marginal profit function. (c) What is the marginal profit when x-10?! (d) What does this marginal profit tell you? (e) Find the level of demand at which profit is a maximum. Show how you do this using calculus. (1) What is the maximum profit, and what is the selling price that realizes this profit? Ans: R(x)-300x-0.02x², P(x)=-0.12x² +288x-200, P'(10) - 285.6 (S), approximate increase in profit from selling one more unit when sales are at 10 units, solving P'(x)-0 gives max at unit. x-1200 units, max profit - $172,600, price = 300-0.02(1200)-$276 per3. Suppose that the total revenue function for a commod- ity is R = 64x- 0.02x². (a) Find R(100) and tell what it represents. (b) Find the marginal revenue function. (c) Find the marginal revenue at x = 100 and tell what it predicts about the sale of the next unit and the next 3 units. (d) Find R(101) - R(100) and explain what this value represents.The demand for q units of a product depends on the price p (in dollars) according to 512 P q= - 1, for p > 0. Find and explain the meaning of the instantaneous rate of change of demand with respect to price when the price is as follows. (a) $16 (b) $64 Interpret the instantaneous rate of change. O If price decreases by the absolute value of this amount, the demand will drop by 1 unit. O If price increases by $1, the demand will increase by the absolute value of this number of units. If price decreases by $1, the demand will drop by the absolute value of this number of units. If price increases by the absolute value of this amount, the demand will drop by 1 unit. If price increases by $1, the demand will drop by the absolute value of this number of units. Interpret the instantaneous rate of change. O If price decreases by the absolute value of this amount, the demand will drop by 1 unit. O If price increases by $1, the demand will increase by the absolute value of this number of units.…
- 7. A paint store sells 270 pails of paint per month at a price of $32 each. A customersurvey indicates that for each $1.20 decrease in price, sales will increase by 6pails of paint.(a) Determine the demand, or price, function.(b) Determine the revenue function (using (a)).(c) Determine the marginal revenue function.(d) Solve R’(x) = 0. Interpret the meaning of this value for this situation.(e) What is the price that corresponds to the value found in part (d)?(a) At what output is the firm’s profit maximised and How much profit is made at this output? (b) Draw the total profit TΠ curve over the range of output where positive profit is made. (d) How much is total fixed cost, At what output is the price elasticity of demand equal to -1 and At what outputs does the firm break even?2. The relationship between price and demand per month for a consumer product is p = 3500 -1.1D5 where p is the price per unit in dollars and D is the demand in units. The fixed cost is $300 per month and the variable cost is $4.00 per unit. What is the optimal number of units that should be produced and sold per month? a. b. What is the maximum profit per month?
- The following graph illustrates the weekly demand curve for motorized scooters in Roanoke. 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) 260 240 220 200 180 160 140 120 100 80 60 40 20 0 0 9 18 27 A X B Demand 36 45 54 63 72 81 QUANTITY (Scooters) 90 99 108 117 Total Revenue ?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 ?Total Total Revenue Cost Quantity (TR) (TC) Profit (MR) (MC) 0 0 8 1 8 10 2 16 11 3 24 13 4 32 16 5 40 20 6 48 27 7 56 36 8 64 47 9 72 65 10 80 90 Marginal Marginal Revenue Cost Fill in the table to determine the profit maximizing level of output, price, and profit. The optimal quantity is A/ A (number) units, the optimal price is (number) dollars, which maximizes (number) dollars. This table A profits at displays profit maximization under the (perfect competition / monopolistic competition / oligopoly / monopoly) market structure.
- (a) What is the profit-maximizing level of output and how much daily profit will the producer below earn if the price of pizza is $ 2.50 per slice? MC S/slice ATC AVC 2.50 1.40 slices/day 570One of South Africa’s cellphone operators, Cell C, is changing their overall business strategy.The focus is now on providing customers with “affordable and accessible services." To do thisthey need your economic expertise.They know that when price for premium services increases from R2/minute to R2.2/minute thedemand for their services falls from 12 customers to 10 customers. Question: What recommendations can you make to increase total revenue?(a) How many vacuums are supposed to be sold to achieve break even? (b) If Primark wants to earn a profit of $36,000, how many vacuum must be sold?