he cost structure for iPhones are as follows, fixed cost of $25 and variable cost per unit of $2. The associated demand function is p = 20 − q . (i) Obtain an expression for the profit, π(q). (ii) Find the range of output which gives a profit of at least $31.
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1) a) Solve the following inequalities:
(i) 5(11 − ?) < ? + 49
(ii) 7? − 3 <
10m + 2
3
< 8 − 5m
(iii) ?
2 ≥ 15 − 2?
b) The cost structure for iPhones are as follows, fixed cost of $25 and variable cost per
unit of $2. The associated demand function is
p = 20 − q .
(i) Obtain an expression for the profit, π(q).
(ii) Find the range of output which gives a profit of at least $31.
c) Use Microsoft Word or Excel to solve the system of linear inequalities:
r + 5t ≤ 5
7t – 2r ≤ 4
r ≥ 0
(NB: clearly identify the solution set by placing a BIG enough ‘S’ to cover
that entire region).
Step by step
Solved in 3 steps
- a.The cost structure for iPhones are as follows, fixed cost of $25 and variable cost per unit of $2. The associated demand function is p = 20 − q . (i) Obtain an expression for the profit, π(q). (ii) Find the range of output which gives a profit of at least $31. b.Classify the following sequences: (i) 6.5, 9.75, 13, 16.35,…….. (ii) 4 ,8 , 16 , 33 ……… 9 9 9 9 c. Given that a geometric progression has a = -2 and r = -0.5, Determine values for the:(i) fifth term of the GP. (ii) sum of the first 20 termsThe monthly demand equation for an electric utility company is estimated to be p=55- (105)x, where p is measured in dollars and x is measured in thousands of killowatt-hours. The utility has fixed costs of $1,000,000 per month and variable costs of $27 per 1000 kilowatt-hours of electricity generated, so the cost function is C(x)=1-10° +27x. (a) Find the value of x and the corresponding price for 1000 kilowatt-hours that maximize the utility's profit. (b) Suppose that the rising fuel costs increase the utility's variable costs from $27 to $39, so its new cost function is C₁(x)=1.10° +39x. Should the utility pass all this increase of $12 per thousand kilowatt-hours on to the consumers?Given Cost and Price (demand) functions C(q) = 110q + 45000 and p(q) = - 2.8q + 800, what profit can be earned if the price is set to be $550 per item? U The profit is $ 1,?9 (Round to the nearest cent.) A company produces a special new type of TV. The company has fixed costs of $499,000, and it costs STT00 to produce each TV. The company projects that if it charges a price of $2300 for the TV, it will be able to sell 850 TVs. If the company wants to sell 900 TVs, however, it must lower the price to $2000. Assumo a linear demand. What is the marginal profit if 200 TVs are produced It is $ 0 per item. (Round answer to nearest dollar.)
- A company manufactures and sells x cellphones per week. The weekly price-demand and cost equations are given below. p=600-0.1x and C(x)= 15,000+ 130x (A) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly revenue? What is the maximum weekly revenus? The company should produce phones each week at a price of $ (Round to the nearest cent as needed.) The maximum weekly revenue is S. (Round to the nearest cent as needed.) (B) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly profit? What is the maximum weekly profit? The company should produce phones each week at a price of $ (Round to the nearest cent as needed.) The maximum weekly profit is $ (Round to the nearest cent as needed.)A business has found that it can sell 750 items if it sets its price to $63.61. However, if it lowers its price to $45.95, it can sell 950 items. (a) Find the linear demand equation (price function) for selling x items. (round to 4 decimal places) p(x) = It costs the business $6.8 per item to produce and they have $3,600 in overhead each mc (b) Find the linear Cost, and quadratic Revenue and Profit functions for producing/selling x items: (round to 4 decimal places) C (x) = Number R(x) = P(x) = Number = Number x+ Number x + Number x² + Number x+ Number + Number (c) How many items should the company sell to break even? What price should they set to so? (lower quantity) They could sell Number (higher quantity) They could sell Number items at a price of $ Number items at a price of $ Number. Submit Assignment Quit & Save each OR each Back QuesThe total cost and the total revenue (in dollars) for the production and sale of x ski jackets are given by C(x)=26x +18,625 and R(x)-200x-0.2x² for 0≤x≤ 1000. (A) Find the value of x where the graph of R(x) has a horizontal tangent line (B) Find the profit function P(x). (C) Find the value of x where the graph of P(x) has a horizontal tangent line. (D) Graph C(x), R(x), and P(x) on the same coordinate system for 0sxs 1000. Find the break-even points. Find the x-intercepts of the graph of P(x) (A) R(x) has a horizontal tangent line at x =
- ect of the utility commission's ruling on the profitability of the firm? 15 A company estimates that the demand for its product fluctuates with the price it charges. The demand function is q = 280,000 – 400p where q equals the number of units demanded and p equals the price in dollars. The total cost of producing q units of the product is estimated by the function C = 350,000 + 300q + 0.0015q? (a) Determine how many units q should be produçed in order to maximize annual profit. (b) What price should be charged? (c) What is the annual profit expected to equal? 16 Solve the previous exercise, using theA large wood products company is negotiating a contract to sell plywood overseas. The fixed cost that can be allocated to the production of plywood is $800,000 per month. The variable cost per thousand board feet is $155.50. The price charged will be determined by p=$600−(0.05)D per 1,000 board feet. a. For this situation, determine the optimal monthly sales volume for this product and calculate the profit (or loss) at the optimal volume. b. What is the domain of profitable demand during a month?The HAC at Humberview has decided to sell Gatorade to raise money. The demand function is described by px=-4x+340 , where x is the number of bottles, in hundreds, and px is in dollars. The cost function, in dollars, is described by Cx=300x-275. Determine the number of Gatorade bottles they must sell so that they maximize their profit.
- A company produces and sells hair dryers in a market where price (p) and demand (D) are related follows: p= $35 + (3,000)/D –- (4,800)/D? The fixed cost (C;) is $800 per month and the variable cost per hair dryer (c,) is $38. With reference to the company in Question 1, assume price and demand are unrelated. The company sells the hair dryers for $80 each if they spend $8,000 per month on advertising (C.). C; and c, remain as indicated in Question 1. The maximum production capacity is 5,000 hair dryers per month. a) What is the demand breakeven b) Is the company's demand breakeven point (in %) more sensitive to 10% increase in sales price or 20% reduction in variable costs? Explain your answer.(1) A company in Scotland bottles sparkling water. The fixed cost per month to produce bottled water is $35,000, and the variable cost is $0.2 per bottle. Price is related to demand according to the following equation: v = 4,000 – 1.1p Determine the optimal price using a nonlinear profit analysis. (2) A tailor on Savile Row is producing suits. The fixed cost per month producing suits is $13,000, and the variable cost is $140 per suit. Price is related to demand, according to the following equation. v = 600 – 1.5p Determine the optimal price using a nonlinear profit analysis.A large company in the communication and publishing industry has quantified the relationship between the price of one of its products and the demand for this product as Price=160−0.02×Demand for an annual printing of this particular product. The fixed costs per year (i.e., per printing)=$47,000 and the variable cost per unit=$40. What is the maximum profit that can be achieved? What is the unit price at this point of optimal demand? Demand is not expected to be more than 4,000 units per year. The maximum profit that can be achieved is $? (Round to the nearest dollar.) The unit price at the point of optimal demand is $? per unit.
