An engineering firm recently conducted a study to determine its benefit and cost structure (total cost). The results of the study are as follows: The total benefit from producing q units is TB(q) = 15,000q- 15q² so that its marginal benefit is %3D MB(q) = 15,000- 30q and the total cost of producing q units is TC(q) = 687,500+10q? so that its %3D marginal cost is MC (q) = 20q %3D 1. Find the level of output q that yields the maximum profit.
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- A company produces two different versions of a certain product. Let q₁ indicate the amount produced of the first version. The cost function c(q₁) for the first version (expressed in euros) can be described by the equation c(q₁) = 9₁ · √√0.59² +59₁ 10 a) For which value(s) of q₁ is the instantaneous rate of change of the cost function equal to 1.75? You may use the graphical calculator to find zeros of a polynomial function if needed. b) Using the result from a), give a precise economic meaning for the instantaneous rate of change of 1.75. We now denote 92 as the amount produced of the second version. The equation of the cost function c(9₂) for the second version is unknown. We do know that the current cost for a production of 2 units of the second version is 50 monetary units and that the elasticity of the cost in terms of the produced amount when 92 = 2 is equal to 1.88. c) Give a linear approximation ƒ of the cost function c(9₂) for production amounts close to q₂ = 2.A division of a company produces income tax apps for smartphones. Each income tax app sells for $7. The monthly fixed costs incurred by the division are $20,000, and the variable cost of producing each income tax app is $2. (a) Find the break-even point for the division. (x, y) = (b) What should be the level of sales in order for the division to realize a 15% profit over the cost of making the income tax apps? (Round your answer up to the nearest whole number.)income tax appsA marginal cost fiction C'(q) is given in the figure below. If the fixed costs are $10,000, estimate: a) the total cost to produce 20 units (use left and right hand sums) b) the additional cost if the company increased production from 20 to 40 units
- Estimate the cost of expanding a planned new clinic by 25,000 ft2. The appropriate capacity exponent is 0.62, and the budget estimate for 185,000 ft2 was $17 million.Given = TC = f(q) = 0.3q2 -105q + 120,000 What volume should be produced for minimum cost? What is the minimum cost?The IT department allocates indirect costs to user departments on the basis of CPU time at the rate of $2000 per second. For the first quarter, the two heaviest use departments logged 900 and 1300 seconds, respectively. If the IT indirect budget for the year is $19.56 million, the percentage of this year’s allocation consumed by these departments is closest to: (a) 22.5% (b) 32% (c) 55% (d) 67%
- A construction crew (that is currently unemployed and receiving $10/hr. in benefits) to fix a road. The cement is purchased from a rip-off monopolist that charges $10/bag more than anyone else. The Follow-up maintenance will be done after 1 year, using a different crew that we will assume is not unemployed. We will also assume the interest rate is 7%. The cost estimate provided by the contractor’s accountant is given in the table below: ITEM Quantity Wage Price Total Labor 1,000 hours $20/hour $20,000 Cement 500 $50 $25,000 Follow up maint. 500 $20/hr $10,000 Project Total $55,000 The opportunity cost of the project is Group of answer choices $55,000 $41,000 $39,000 $33,000A study of 86 savings and loan associations in six northwestern states yielded the following cost function. C� = 2.38 - 0.006153Q� + 0.000005359Q2�2 + 19.2X1�1 (2.86) (3.08) (3.68) (2.96) where C� = average operating expense ratio, expressed as a percentage and defined as total operating expense ($ million) divided by total assets ($ million) times 100 percent. Q� = output; measured by total assets ($ million) X1�1 = ratio of the number of branches to total assets ($ million) Note: The number in parentheses below each coefficient is its respective t-statistic. Which of the variable(s) is (are) statistically significant in explaining variations in the average operating expense ratio? (Hint: t0.025,70=1.99�0.025,70=1.99.) Check all that apply. Q� Q2�2 X1�1 What type of average cost-output relationship is suggested by these statistical results? Quadratic Cubic Linear Based on these results, what can we…A study of 86 savings and loan associations in six northwestern states yielded the following cost function. C = 3.12 - 0.006768Q + 0.000005359Q2 +21.1X1 (3.12) (2.61) (2.89) (2.96) where C = average operating expense ratio, expressed as a percentage and defined as total operating expense ($ million) divided by total assets ($ million) times 100 percent. Q = output; measured by total assets ($ million) X1 = ratio of the number of branches to total assets ($ million) Note: The number in parentheses below each coefficient is its respective t-statistic. Holding constant the effects of bank branching (X1), what is the level of total assets that minimizes the average operating expense ratio? $1,262.92 million $1,558.81 million $631.46 million $460.99 million What is the average operating expense ratio for a savings and loan association with the level of total assets determined in the previous part and 1 branch? 1.17% 3.15% 1.02% 5.63% What is the ratio with 10 branches instead? 5.93% 1.47%…
- A study of 86 savings and loan associations in six northwestern states yielded the following cost function. C� = 3.69 - 0.007999Q� + 0.000005359Q2�2 + 25.0X1�1 (3.69) (3.08) (3.42) (3.50) where C� = average operating expense ratio, expressed as a percentage and defined as total operating expense ($ million) divided by total assets ($ million) times 100 percent. Q� = output; measured by total assets ($ million) X1�1 = ratio of the number of branches to total assets ($ million) Note: The number in parentheses below each coefficient is its respective t-statistic. Holding constant the effects of bank branching (X1�1), what is the level of total assets that minimizes the average operating expense ratio? $746.31 million $1,562.70 million $1,492.63 million $461.31 million What is the average operating expense ratio for a savings and loan association with the level of total assets determined in the previous part and 1 branch?…Two new rides are being compared by a local amusement park in terms of their annual operating costs. The two rides would generate the same level of revenue (thus the focus on costs). The Tummy Tugger has fixed costs of $10,000 per year and variable costs of $2.50 per visitor. The Head Buzzer has fixed costs of $4000 per year and variable costs of $4 per visitor. (a) Mathematically find the number of visitors per year for the two rides to have equal annual costs. (b) Develop a breakeven graph to show: • Accurate total cost lines for the two alternatives (show line, slopes, and equations). • The breakeven point for the two rides in terms of number of visitors. • The ranges of visitors per year where each alternative is preferred.Until recently, hamburgers at the city sports arena cost $2.50 each. The food concessionaire sold an average of 1,375 hamburgers on game night. When the price was raised to $3.00, hamburger sales dropped off to an average of 1,250 per night. The concessionaire's fixed costs were $1,133.60 per night and the variable cost was $2.60 per hamburger. Answer the following questions (A) through (F). (A) Assume that the relationship between price p and demand x is linear. Express p as a function of x and find the domain of this function. p=nothing The domain of p is nothing. (Type a compound inequality.) (B) Find the revenue function in terms of x and state its domain. R(x)=nothing The domain of R(x) is nothing. (Type a compound inequality.) (C) Assume that the cost function is linear. Express the cost function in terms of x. C(x)=nothing (D) Graph the cost function and the revenue function in the same coordinate system. Choose the correct graph below. Find the…