production process

The Goodparts Company produces a component that is subsequently used in the aerospace indus- try. The component consists of three parts (A, B, and C) that are
purchased from outside and cost 40, 35, and 15 cents per piece, respectively. Parts A and B are assembled first on assembly line 1, which produces 140 components
per hour. Part C undergoes a drilling operation before being finally assembled with the output from assembly line 1. There are in total six drilling machines, but
at present only three of them are operational. Each drilling machine drills part C at a rate of 50 parts per hour. In the final assembly, the output from assembly
line 1 is assembled with the drilled part C. The final assembly line produces at a rate of 160 components per hour. At present, components are produced eight hours
a day and five days a week. Management believes that if need arises, it can add a second shift of eight hours for the assembly lines. The cost of assembly labor is
30 cents per part for each assembly line; the cost of drilling labor is 15 cents per part. For drilling, the cost of electricity is 1 cent per part. The total
over- head cost has been calculated as \$1,200 per week. The depreciation cost for equipment has been calculated as \$30 per week. a. Draw a process flow diagram and
determine the process capacity (number of components produced per week) of the entire process. b. Suppose a second shift of eight hours is run for assembly line 1
and the same is done for the final assembly line. In addition, four of the six drilling machines are made operational. The drilling machines, however, operate for
just eight hours a day. What is the new process capacity (number of components produced per week)? Which of the three operations limits the capacity? c. Management
decides to run a second shift of eight hours for assembly line 1 plus a second shift of only four hours for the final assembly line. Five of the six drilling
machines operate for eight hours a day. What is the new caecity? Which of the three operations limits the capacity? d. Determine the cost per unit output for
questions b and c. e. The product is sold at \$4.00 per unit. Assume that the cost of a drilling machine (fixed cost) is \$30,000 and the company produces 8,000
units per week. Assume that four drilling machines are used for production. If the company had an option to buy the same part at \$3.00 per unit, what would be the
break-even number of units?

simplex method (fundamental insight)
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production process

Q1. Cally uses labour (L) and capital (K) in her production process. The wage rate for one unit of labour is \$10, while units of capital cost \$20 per unit.

a. Graphically depict the isocost line for Cally’s firm for a \$12,000 expenditure by Cally on inputs. Draw a typical Cobb-Douglas isoquant for an output level to depict the optimal levels of L and K for quantity Qo and TCo = \$12,000. Make sure all relevant points on your diagram are identified. [4 marks]

b. The provincial government has decided that a minimum hourly wage for labour should be of \$12 per hour. In the short-run, with capital fixed at K, show graphically what happens to total cost when Cally continues to produce Qo and explain why. [6 marks]

c. Show the optimal factor mix the Cally will use in the long-run to produce Qo given the change in the wage rate, also explain your answer. [6 marks]

Q.2 Chunzheng’s production function is given by:

Q = K^2L

a. What are the returns to scale associated with Chunzheng’s production function? Prove your answer. [4 marks]

b. Derive Chunzheng’s input demand curves for labour and capital when w is the wage for labour and r is the rental cost of capital? [6 marks]

c. The wage rate is w = 10 and the rental rate of capital is r = 20. Suppose the firm wants to produce 27,000 units of output. What is the most efficient combination of labour and capital (L, K)? [4 marks]

d. Given your results from above, what is the equation for the Chunzheng’s long-run total cost curve as a function of quantity Q. How much does it cost to produce 27,000 units? [4 marks]