a) R'(Q) = 28Q - e b) R'(Q) 10(1+Q)-² find in each case the total-revenue function R (Q). What initial condition can you introduce to definitize the constant of integration? =
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- Use the functions given below to solve the problem. C(x) represents the cost, in dollars, of x units of a product and R(x) represents the revenue, in dollars, from the sale of x units. Find the number of units that must be produced and sold in order to break even, C(x) = 72,000 + 43x and R(x) = 47x The number of units that must be produced and sold in order to break even is units.1) Economic Application of Integrals. Given the following marginal-revenue functions: a) R'(Q) = 28Q – e b) R'(Q) = 10(1+Q)-2 find in each case the total-revenue function R (Q). What initial condition can you introduce to definitize the constant of integration?As a producer and seller of some commodity, you have learned that, if you produce and sell x itmes in a particular month, the following functions can be used to find the cost and revenue: Revenue: R(x)=150x-x^2 and Cost: C(x)=3000+20x. (a) Write a simplified formula for your profit in a particular month, P(x)=R(x)- C(x) (b) Find the "break-even" point(s) (c) How many items should you produce and sell in a month in order to achieve a maximum profit? (d) What is the maximum possible monthly profit? This is the problem and I cannot solve the c and d, could you please help me?
- The profit of a company, in dollars, is the difference between the company's revenue and cost. The cost, C(x), and revenue, R(x), are functions for a particular company. The x represents the number of items produced and sold to distributors. C(x)=-2300+40x R(x)=840x-x² a) Determine and simplify the profit function. Write your answer in descending order. P(X)-The marginal profit for a certain company is MP₁(x) = -x² + 18x-45. The company expects the daily production level to rise from x = 3 to x = 5 units. The management is considering a plan that would have the effect of changing the marginal profit to MP₂(x)= -x² +14x-33. Should the company adopt the plan? Determine the area between the graphs of the two marginal profit functions from x = 3 to x = 5. Interpret this area in economic terms. C Should the company adopt the plan that would make the marginal profit be MP₂? O A. Yes, because the company will make a larger profit under the new plan. B. No, because the company's profit will be smaller under the new plan. O C. It is impossible to tell using the given information. The area between the graphs of the two marginal profit functions from x = 3 to x = 5 is sq. units.4. Determine the average function and the marginal function for each of the following functions Totals: a) Total income TR = 100 Q - Q2 b) Total cost TC = 1000+ 10 Q + .01 Q2 c) Total profit TP = 50 Q - 0.1 Q2 - 1000
- A factory makes bicycle tires. The cost, C, in dollars and revenuue in dollars, R, are both functions of the number of tires, n.a) Describe what is meant by C'(4) = 8b) Generate a mathematical equation, using function notation, to model the following statements: for (b) + (c) "The marginal revune for 15 tires sold decreases by $1."c) "The revenue at 3 tires equals the change in cost at 5 tires"Let p = 23 - Vx and C(x) = 268 + 4x, where x is the number of garden hoses that can be sold at a price of $p per unit and C(x) is the total cost (in dollars) of producing x garden hoses. (A) Express the revenue function in terms of x. (B) Graph the cost function and the revenue function in the same viewing window for 0The marginal revenue (in thousands of dollars) from the sale of x handheld gaming devices is given by the following function. R'(x) = 4x (x²+25,000) (a) Find the total revenue function if the revenue from 120 devices is $34,166. (b) How many devices must be sold for a revenue of at least $50,000? (a) The total revenue function is R(x), given that the revenue from 120 devices is $34,166. (Round to the nearest integer as needed.) (b) devices must be sold to generate a revenue of at least $50,000 (Type a whole number.)E Let the demand function for a product be given by the function D(q) = -1.65g + 270, where q is the quantity of items in demand and D(q) is the price per item, in dollars, that can be charged when q units are sold. Suppose fixed costs of production for this item are $4, 000 and variable costs are $3 per item produced. If 96 items are produced and sold, find the following: A) The total revenue from selling 96 items (to the nearest penny). Answer: $ B) The total costs to produce 96 items (to the nearest penny). Answer: $ C) The total profits to produce 96 items (to the nearest penny. Profits may or may not be negative.). Answer: $ Question Help: C ME PE Video 66°F Mostly cloudyDoes the output maximization level of input use exist for the following function? If yes, then what is the exact input-use level? y = x1 + 0.1x12 - 0.05x13 + x2 + 0.1x22 - 0.05x23The total cost of producing 1 unit of a product is ху C(x, y) = 28 + 4x + 6y + 56 dollars where x is the cost per pound of raw materials and y is the cost per hour of labor. (a) If labor costs are held constant, find the function that describes the rate at which total cost increases for each increase of $1 per pound in material cost. (b) If material costs are held constant, find the function that describes the rate at which total cost increases for each $1 per hour increase in labor costs.SEE MORE QUESTIONS