8. A commodity has price demand function p(x)= 11800 - .01x and each unit costs 1000 and the overhead is 5000. a) what is the revenue function, cost function and profit function ? b) what price should be charged to maximize profits? c) what is the marginal profit for x=400 ? Explain what this marginal profit number means.
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- 6. Heidi owns a business that sells photographs. The profit function for her business can be modelled by the equation p(x)=-0.5x2-5x-7, where x is the quantity sold, in thousands, and P(x) is the profit in thousands of dollars. How many photos must Heidi sell in order for her business to break even? please type answer, not in writingTotal revenue for producing 10 units of output is $5. Total revenue for producing 11 units of output is $9. Given this information, the Average revenue for producing 11 units is $2. Average revenue for producing 11 units is $4 Marginal revenue for producing the 11th unit is $2. Marginal revenue for producing the 11th unit is $4.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?
- 1.The price p in dollars of a certain commodity and the quantity x sold obey the demand equation p= -1/5x + 200 where 0<=x <=1000. Suppose that the cost C in dollars of producing x units is C= the square root of x divided by 10 + 400. Assuming that all items produced are sold, find the cost of c as a function of the price p.Exercises: 1 Given the demand (price) and cost functions P=2000-40Q and C(Q) = 3000+400Q respectively, find the following, using the calculus approach: a. Profit-maximizing output (quantity) b. Profit-maximizing price c. Maximum profit value d. Revenue maximize QuantityIf the demand for a particular commodity is p=-0.09x+51 the total cost function, C(x)=1.32x^2+11.7x+101.4 where x is the level of production. Find the 1. Revenue, R(x) 2. Profit, S(x) 3. All the values of x for the production of the commodity are profitable.
- Assume that a firm’s marginal revenue curve intersects the rising portion of its marginal cost curve at 500 units of output. At this output level, a profit-maximizing firm’s total cost of production is $1,000. If the price of the product is $5 per unit, the total revenue earned by the firm will be:Question 6 options: The price of a product in a competitive market is $100. The cost per unit of producing the product is c=50+.1x, where x is the number of units produced each month. Find a) The monthly revenue R(x) b) The monthly cost function C(x) c) The monthly profit function P(x) d) Find x such that profit is maximized, and find the maximum profitA manufacturer of upholstery can sell 2121 yards of fabric at a price of $3.11$3.11 per yard. If the price is $1.85$1.85, she can sell 3535 yards. The total cost of manufacturing x yards of fabric is C(x)=0.6x+36C(x)=0.6x+36 dollars. Step 1 of 3 : Assuming the demand function is linear, find an equation for D(x)D(x). Do not round your answer.
- Explain why a firm might want to produce its good even after diminishing marginal returns have set in and marginal cost is on the rise. People often believe that large firms in an industry have cost advantages over small firms in the same industry. For example, they might think a big oil company has a cost advantage over a small oil company. For this to be true, what condition must exist? Explain your answer.Assume that the marginal revenue equals rising marginal cost at 100 units of output. At this output level, a profit-maximizing firm's total fixed cost is $700 and its average variable costs are $5. If the price of the product is $4 per unit and the firm produces the profit-maximizing level of output, How much profit firm will earn ?For a firm’s product, the demand function is p =72−0.04q and the average cost function is i. ¯ c = 500 q +30 i. At what level of output would profit be maximized? ii. ii. Atwhat price is the profit maximized?