In the accompanying figure, labor costs $60 per unit. The manager wants to produce 2,500 units of output. The optimal input (labor-capital) combination involves units of capital. Capital (K) 90 חי E C B A Q = 2,500 0 10 20 30 40 50 60 Labor (4)
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- The amount of fish caught per week on a trawler is a function of the crew size assigned to operate the boat. Based on past data, the following production schedule was developed: CREW SIZE (NUMBEROF WORKERS) AMOUNT OF FISH CAUGHT PERWEEK (HUNDREDS OF LBS) 2 3 4 5 6 7 8 9 10 11 12 3 6 11 19 24 28 31 33 34 34 33 a. Over what ranges of workers are there (i) increasing, (ii) constant, (iii) decreasing, and (iv) negative returns?b. How large a crew should be used if the trawler owner is interested in maximizing the total amount of fish caught?c. How large a crew should be used if the trawler owner is interested in maximizing the average amount of fish caught per worker?The amount of fish caught per week on a trawler is a function of the crew size assigned to operate the boat. Based on past data, the following production schedule was developed: CREW SIZE (NUMBEROF WORKERS) AMOUNT OF FISH CAUGHT PERWEEK (HUNDREDS OF LBS) 2 3 4 5 6 7 8 9 10 11 12 3 6 11 19 24 28 31 33 34 34 33 a. Over what ranges of workers are there (i) increasing, (ii) constant, (iii) decreasing, and (iv) negative returns?b. How large a crew should be used if the trawler owner is interested in maximizing the total amount of fish caught?c. How large a crew should be used if the trawler owner is interested in maximizing the average amount of fish caught per worker? Expert Solution arrow_forward Step 1 The marginal and average product of the worker or labor is useful in calculating the amount of fish that the workers can catch as well as in the real industries also. If the company calculates the average and marginal products, the company can decide on how to…A firm has the following production function: Q = 9L2/3K1/3 Where Q is output, L is labor and K is Capital. Where Q is output, L is labor and K is Capital. (a) What sort of returns to scale characterize this production function? (b) Derive the marginal product of labor and capital. (c) What do we mean when we say the production function is linearly homogenous?
- The pumlative eveage labor hours to assemble the first fiva units of product A was 14.579 hours. If the learning curve, based on the previous experience with similar products, is 76%, what is the estlimated tlime (labor hours hat wil be neguirees its assemtie ife 2 uni? The mumiber of labor hours required to assemble the 24 unit is hours. (Round to one decimal place.)Ben's swim coach estimates that his time, t, in the 100-yard butterfly at a big upcoming meet as a function of the number of yards he swims per week, y, is t = 50+8e-0.00005y Based on this production function, his coach also estimates that if Ben swims 20,000 yards per week, his time will be 52.94 seconds, and he will finish tenth place. If he swims 40,000 yards per week, his time will be 51.08 seconds, and he will come in third. If he swims 60,000 yards per week, his time will be 50.40 seconds, and he will win the meet. Use calculus to determine Ben's marginal productivity of time given the number of yards he practices. Is there diminishing marginal productivity of practice yards? Ben's marginal productivity of swim time given y practice yards (MP) is (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with the ^ MPy character.)JayZee is the new sensation in the fashion industry, his cloth line is being appreciated and liked by the masses. Due to increased demand he decided to hire more labour (variable factor) while it is not possible for him to extend his warehouse size. If he hires you as an expert to ensure maximum profits with following information, take the best decisions, solve all the parts and their subparts as well. Total Product Units of Capital Units of Labour 0 5 0 100 5 1 240 5 2 400 5 3 500 5 4 560 5 5 570 5 6 570 5 7 520 5 8 460 5 9 1. Find: AP, MP and TR (show calculation)2. Find: i. Identify the three stages of production. ii. Construct the curves of TP, MP and AP. iii. Suggest how many labour should JayZee hire and why.
- Total Fixed Total Variable Labor (workers) (units per day) Output Cost cost (dollars) (dollars) 20 20 25 50 1 2 3 715 13 16 20 20 100 4. 5. 18 20The amount of fish caught per week on a trawler is a function of the crew size assigned to operate the boat. Based on past data, the following production schedule was developed: Crew size 2 3 4 5 6 7 8 9 10 11 12Fish caught (100 lbs/week) 3 6 11 19 24 28 31 33 34 34 33 b) How large a crew should be used if the trawler owner is interested in maximizing the total amount of fish caught?c) How large a crew should be used if the trawler owner is interested in maximizing the average amount of fish caught per person?d) Suppose the owner can sell all the fish caught for $75 per 100 pounds and can hire as many crew members as desired by paying them $150 per week. Assuming that the owner of the trawler is interested in maximizing profits, determine the optimal crew size.JayZee is the new sensation in the fashion industry, his cloth line is being appreciated and liked by the masses. Due to increased demand he decided to hire more labour (variable factor) while it is not possible for him to extend his warehouse size. If he hires you as an expert to ensure maximum profits with following information, take the best decisions, solve all the parts and their subparts. Total Product Units of Capital Units of Labour 0 5 0 100 5 1 240 5 2 400 5 3 500 5 4 560 5 5 570 5 6 570 5 7 520 5 8 460 5 9 1. Find: AP, MP and TR (show calculation)2. Find: i. Identify the three stages of production. ii. Construct the curves of TP, MP and AP. iii. Suggest how many labour should JayZee hire and why.
- Q4 A business manager determines that t months after production begins on a new product, the number of units produced will be P thousand,where P(t) =6?2 + 5? /(? + 1)2 production in the long run (i) A ruptured pipe in a North Sea oil rig produces a circular oil slick that is y meters thick at a distance x meters from the rupture.Turbulence makes it difficult to directly measure the thickness of the slick at the source (where x = 0),but for x > 0,it is found that y =0.5(x2 + 3x)/ x3 + x2 + 4x Required:a)Assuming the oil slick is continuously distributed,how thick would you expect it to be at the source?10K L%. 1). Consider the production function Q = (a) What is the output when K = 100000 and L = 243? (b) Use the marginal analysis to estimate Q(99995, 243) and Q(100000, 245). (c) Use a calculator to compute these two values of Q to three decimal places and compare these values with your estimates in (b). (d) How big must AL be in order for the difference between Q(100000, 243+AL) and its linear approximation Q(100000, 245) + -DAL, to differ by more than two units?Total Fixed Total Variable Labor Output (workers) (units per day) (dollars) Cost Cost (dollars) 20 20 20 20 20 20 25 50 75 100 125 2 19 13 4. 16 1S
