15. The marginal profit in dollars on Brie cheese sold at a cheese store is given by P'(x) = x (20x + 60x) , where x is the amount of cheese sold, in hundreds of pounds. The "profit" is - $50 when no cheese is sold. a. Find the profit function. b. Find the profit from selling 300 pounds of Brie cheese.
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- 13. The marginal profit for the new X-99 pogo stick is P'(x) = -0.1x+ 60 where x is the number of sticks produced and sold. The profit is - $1000 when 50 sticks have been produce and sold. a) Find the profit function. b) What level of production of pogo sticks (x) produces a maximum profit?8. Daisy's Doggie Treats has a marginal profit function given by m(x) = 0.34e0.02x dollars per bag of treats, where x is the number of bags of treats produced and sold each month. If production and sales increase from 200 to 250 bags each month, then profit will increase by which of the following? a) $31.90 b) $1,594.86 c) $72,242.76 d) $1,653.27 e) None of the aboveYou are selling ice cream bars from a cart. You sell them for $0.75 per bar. Your cost for the ice cream is $0.30 per bar, and your cost for the rental of the cart is $50.a) Write a formula for your profit from selling ice cream bars. Be sure to identify all yourvariables and the units used.b) What is the slope of the profit function? What is its meaning in terms of selling icecream bars?c) What is the vertical intercept of the profit function? What is its meaning in terms ofselling ice cream bars?d) What is the horizontal intercept of the profit function? What is its meaning in termsof selling ice cream bars?
- you are an accountant for a manufacterer of radios. the demand function for the tablets is p= 40-4x2 where x is the number of tablets produced in millions. it costs the company $15 to make a tablet. write an equation for the manufactures profit as a function of the number of tablets produced. the company currently produces 1 million tablets and makes a profit of $21000000, but you would like to scale up production a bit, what greater number of tablets could the company produce to yield the same profitQuestion 16 Referring to Figure 1 in Question 14, When the price of the good is $175, the firm's maximum profit is (leave out the dollar sign)1) What is total cost at the profit-maximizing quantity? 2) What is the profit at the profit-maximizing quantity? 3) What is total variable cost at the profit-maximizing quantity?
- Funny Bunny is considering installing ice-cream stalls on Turtle Beach. The length of the beach is 5 miles long. On average, in a week, there are 1,000 swimmers come to beach and each value an ice-cream at $5. Transportation costs are $2.5. each ice cream costs $0.50 to make and there are $40 overhead costs per stall.1.find the optimal number of stalls for Funny Bunny?2.what is the profit at optimal number of stalls?Bill runs a business that makes custom-printed towels. It will cost him $8 each to purchase and print on towels, and he will have to pay a rent of $1,700 per month for him workshop. Based on market research, Bill estimates that he can sell custom towels for $25 each. a) Calculate the number of towels he needs to sell per month to break-even. towels b) Calculate the break-even in dollars (round off to the nearest cent).Q.5 A firm is making two products A & B. Each unit of A incurs a cost of production to the tune of $150 and that of B incurs a cost of $200. Product A earns a profit of $15/unit and B gets $20/unit. The estimated monthly demand of both A & B is at maximum 500 units. Monthly production budget is set at $50,000.How many units of A & B should the firm make in order to maximize profit. Conduct sensitivity analysis and answer the following questions: 1. State the optimal solution. 2. What is the objective function value? 3. Find out the range of profit for A in the objective function for which the above solution remains optimal. 4. Which constraint/s is/are binding? 5. Interpret the shadow price for production budget.
- 1. Let a firm’s cost function be c(y1, y2) = F + αy1y2 + y21 + y22, where α is some constant.a) What restriction on α is required to guarantee that this cost function exhibits economies ofscope?b) What restriction on α is required to guarantee that this cost function exhibits cost complementarities in both goods? Note that you’ll need to verify cost complementarities for y1 andy2.2. Given the industry demand function X(p) = 100 − 2p, consider the following scenarios:• The market is a perfectly competitive market. Assume there are identical firms with marginalcost of 12 in this perfectly competitive market.• The market is dominated by one monopolist with a marginal cost of 12. This monopolist isable to achieve 1st degree pricing.• The market is dominated by one monopolist with a marginal cost of 12, but the monopolistis able to achieve only 2nd degree pricing. Assume the menu offers only 2 choices:(Q∗1 = 30, p∗1 = 35), and (Q∗2 = 60, p∗2 = 20).• The market is dominated by one monopolist…D) What is total cost at the profit-maximizing quantity? E) What is the profit at the profit-maximizing quantity? F) What is total variable cost at the profit-maximizing quantity?The following graph plots the marginal cost (MC) curve, average total cost (ATC) curve, and average variable cost (AVC) curve for a firm operating in the competitive market for sun lamps. COSTS (Della) 72 04 8 56 24 16 . 0 Price (Dollars per lamp) MOD 8 12 36 48 60 10 ATC AVC 40 00 QUANTITY (Thousands of lamps) For every price level given in the following table, use the graph to determine the profit-maximizing quantity of lamps for the firm. Further, select whether the firm will choose to produce, shut down, or be indifferent between the two in the short run. (Assume that when price exactly equals average variable cost, the firm is indifferent between producing zero lamps and the profit-maximizing quantity of lamps.) Lastly, determine whether the firm will earn a profit, incur a loss, or break even at each price. Quantity (Lamps) ? Produce or Shut Down? Profit or Loss?