2. Consider the production functions given below: a. Suppose that the production function faced by a bread producer is given by Q = 4KL, where MPK = 4L and MP, = 4K. i. Do both labor and capital display diminishing marginal products in the short run? Explain. ii. Find the marginal rate of technical substitution for this production function. (Hint: The MRTS MPL MPK iii. Does this production function display a diminishing marginal rate of technical substitution? iv. Graph isoquants for Q = 20, and Q = 40. Put capital (K) on the y-axis and labor (L) on the x- axis. Label the isoquants with their quantities. v. What are the returns to scale for this firm? Explain. 20 19 18 17 16 15 14 13 12 11 10 9 0 1 2 3 4 5 6 00 9 10 11 12 13 14 15

2. Consider the production functions given below: a. Suppose that the production function faced by a bread producer is given by Q = 4KL, where MPK = 4L and MP, = 4K. i. Do both labor and capital display diminishing marginal products in the short run? Explain. ii. Find the marginal rate of technical substitution for this production function. (Hint: The MRTS MPL MPK iii. Does this production function display a diminishing marginal rate of technical substitution? iv. Graph isoquants for Q = 20, and Q = 40. Put capital (K) on the y-axis and labor (L) on the x- axis. Label the isoquants with their quantities. v. What are the returns to scale for this firm? Explain. 20 19 18 17 16 15 14 13 12 11 10 9 0 1 2 3 4 5 6 00 9 10 11 12 13 14 15

Essentials of Business Analytics (MindTap Course List)

2nd Edition

ISBN:9781305627734

Author:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Publisher:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Chapter13: Nonlinear Optimization Models

Section: Chapter Questions

Problem 2P: The Cobb-Douglas production function is a classic model from economics used to model output as a...

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The Cobb-Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the form: f(L,C)=c0Lc1Cc2, where c0, c1, and c2 are constants. The variable L represents the units of input of labor, and the variable C represents the units of input of capital. a. In this example, assume c0 = 5, c1 = 0.25, and c2 = 0.75. Assume each unit of labor costs 25 and each unit of capital costs 75. With 75,000 available in the budget, develop an optimization model to determine how the budgeted amount should be allocated between capital and labor in order to maximize output. b. Find the optimal solution to the model you formulated in part (a). (Hint: When using Excel Solver, use the Multistart option with bounds 0 L 3,000 and 0 C 1,000.)
Suppose you are analyzing a firm that is successfully executing a strategy that differentiates its products from those of its competitors. Because of this strategy, you project that next year the firm will generate 6.0% revenue growth from price increases and 3.0% revenue growth from sales volume increases. Assume that the firms production cost structure involves strictly variable costs. (That is, the cost to produce each unit of product remains the same.) Should you project that the firms gross profit will increase next year? If you project that the gross profit will increase, is the increase a result of volume growth, price growth, or both? Should you project that the firms gross profit margin (gross profit divided by sales) will increase next year? If you project that the gross profit margin will increase, is the increase a result of volume growth, price growth, or both?
1. The formula used to calculate the number of units needed in order to earn a target income is a. (Fixed costs + variable costs) / Sales b. (Fixed costs + target income) / Sales c. (Fixed costs + target income) / CM per unit d. (Fixed costs + variable costs) / CM per unit 2. The indifference point is reached when * a. The savings in variable cost is equal to the increase in fixed costs. b. The savings in variable cost is less than the increase in fixed costs. c. The savings in fixed cost is equal to the decrease in variable cost. d. The savings in fixed cost is more than the increase in variable costs.' 3. Which of the following is not an assumption used to prepare a cost-volume-profit graph? * a. Constant sales mix b. Constant cost fluctuations c. Units produced equal units sold d. Liner costs within the relevant range
Which of the following is true of the contribution margin ratio? a.If the contribution margin ratio increases, the price must have decreased. b.If the contribution margin ratio increases, the variable cost ratio decreases. c.It is the proportion of each sales dollar available to cover variable costs. d.If the contribution margin ratio increases, more units must be sold to break even. e.It is complementary to the net profit ratio.
If both the fixed costs associated with a product and the variable costs (as apercentage of sales dollars) decrease, what will be the effect on the contribution margin ratio and the break-even point, respectively?a. Decrease, increase.b. Increase, decrease.c. Decrease, decrease.d. Increase, increase.
Each of a company's two product lines has a different contribution margin ratio . If the company's total sales remain the same but the sales mix shifts toward selling more of the product with the higher contribution ratio , which of the following is true ? O a Fixed cost will be constant . . the breakeven point will decrease . Ocall of the answers are true . d the average contribution margin ratio will increase . O e operating income will increase
If only the selling price per unit of a product increases (variable cost per unit and total fixed costs do not change), does the breakeven point increase or decrease? Using Break Even Analysis, provide a unique mathematical example to support you
(1)Use the graph to answer the question that follows. Based on the chart above, if the product sells at a price of $3 per unit, what is the marginal revenue product of the second unit of labor? A-$30. B-$45. C-$90. D-$120. E-Indeterminate (2)The number of units of output that a machine will produce increases, ceteris paribus. How will this change in productivity affect demand for the machine? A-Demand for the machine will increase. B-Demand for the machine will decrease. C-There will be no change in demand for the machine. D-Demand will not change, but quantity demanded will decrease. E-Demand will not change, but quantity demanded will increase.
Required: A. For each model, compute the contribution margin per unit. B. For each model, compute the contribution margin per Direct Labor hour. C. If there is excess capacity, which model is the most profitable to produce? Why? D. If there is labor crisis, which model is the most profitable to produce? Why?
The break-even point in CVP analysis is defined as the point 1) where output units equal input units. 2) where total revenue equals fixed costs. 3) where revenues less variable costs equal operating income. 4) where the unit contribution margin equals the selling price less the unit variable cost. 5) where total revenue equals total costs.
g) Briefly explain the impact of each of the following scenarios on the contribution margin per unit and the break-even point:(i) Sales volume increases(ii) Total fixed cost decreases(iii) Selling price per unit increases(iv) Variable cost per unit increases
A break-even chart has been set up to show the current break-even point. Due to an increase in the price of raw materials, the variable cost per unit has increased. Assume all other costs and the selling price per unit remains constant. How does this change in the variable cost per unit affect the break-even chart? Select one: a. The y-intercept of the total cost line increases. b. The slope of the total cost line increases. c. The break-even point in units decreases. d. The y-intercept of the total cost line decreases.