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- 100VKL, where q is 4. The production function for puffed rice is given by q = the number of boxes produced per hour, K is the number of puffing guns used each hour, and L is the number of workers hired each hour. (a) Calculate the q = 1,000 isoquant for this production function and show it on a graph. (b) If K = 10, how many workers are required to produce q =1,000? What is the average productivity of puffed-rice workers? (c) Suppose technical progress shifts the production function to q = 200 VKL. Answer parts (a) and (b) for this new situation.It costs a company $58 to produce 6 units of a product and $78 to produce 10 units. Assuming that the cost is linear, how much does it cost to produce 25 units?Suppose that a furniture manufacturer produces tables. The manufacturer's production function is Q(KL)- 2K0.8 0.2 where Kis the number of wood saws and L is the number of labor hours used to produce tables. The prevailing wage rate is $10 per hour and the rental rate associated with wood saws is $50. The manufacturer has a goal to produce 1,000 units. What Lagrangian equation can be used to solve the manufacturer's cost minimization problem? Oa. C = 2K12 s.t. 1,000 = 50K + 10L b. = Oc L = Od. L = 10K + 50L s. t. 1,000 = 2K08102 50K + 10L s.t. 1,000= 2KL02 2K10 s. t. 1,000= 10K + 50L
- Determine the returns to scale for the following production functions. a) ? = K + 7L b) ? = KL3A production process using two inputs, labor and capital, can be written as: Q = 3LK where Q represents output per day (tons). Find the MRTS for this production. It isConsider the production function: Q = 2K + 3L. The MRTSLK is:
- Q4 (i) 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) =6t2 + 5t (t + 1)2. What happens to production in the long run ? (ii) 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.Assuming the oil slick is continuously distributed,how thick would you expect it to be at the source?b) Suppose a company has this Leontief production function Q = min(20K,50L) i) List a few combinations that will produce 500 units of outputA skateboard manufacturer produces skateboards at a cost of $45 each, with a monthly fixed cost of $9000. Let x be the number of boards manufactured in a month. Write a function C(x) that represents the total cost of producing x boards. A/ Write a function A(x) that represents the average cost per skateboard each month. A/ Find the equation of the horizontal asymptote of A(x). A .D
- Compute the MRTS for this production function: Y (K,L) = 2K+5LDoes the output maximization level of input use exist for the following function? If yes, then what is the exact input-use level? y = x1 + 0.1x12 - 0.05x13 + x2 + 0.1x22 - 0.05x23Considering the Production Function Y = 95 - 2X,2 + 3X, + 5X,X2 - 6X22 + 18X2 Find the values of X1:X, and TPP