Assignment 1: Problem 1 1- A company that makes shopping carts for supermarkets recently purchased some new equipment that reduced the labor content of the jobs needed to produce shopping carts. The information regarding the old system (before adding the new equipment) and after adding the new machines are given below. Current System New Equipment Added Output/hr 80 84 Workers 5 4 Wage/hr $10 $10 Machine/hr $40 $50 a) Compute labor productivity for both the Old System and the New System b) Compute AFP productivity for both the Old System and the New System c) Suppose production with old equipment was 30 units of cart A at price of $100 per cart, and 50 units of cart B at price of $120. Also suppose that production with new equipment is 50 units of cart A, at price of $100 per cart, and 30 units of cart B at price of $120. Compare all factor productivity for old and new systems.

Assignment 1: Problem 1 Compute labor productivity Current Situation New Machine Added Output/hr 80 84 Workers 5 4 Wage/hr $10 $10 Machine/hr $40 $50 Compute labor productivity Old System : 80/5 = 16 units/worker New System : 84/4 = 21units/worker Compute all factor productivity Old System : 80/(5*10 + 40) =0 .89 units/$ New System : 84/(4*10+50) = 0.93 units/$

Assignment 1: Problem 1 Now suppose: Production with old equipment was 30 units of cart A at price of $100 per cart, and 50 units of cart B at price of $120. Production with new equipment is 50 units of cart A, at price of $100 per cart, and 30 units of cart B at price of $120. Compare all factor productivity for old and new systems. Old System : [(30)(100)+(50)(120)]/90 = 9000/90 = 100 New System : (50)(100)+(30)(120)]/90 = 8600/90 = 95.6

Assignment 1: Problem 2 Factor Old System New System 2. A company has introduced a process improvement that reduces processing time for each unit, so that output is increased by 25% with less material, but one additional worker required. Under the old process, five workers could produce 60 units per hour. Labor costs are $12/hour, and material input was previously $16/unit. For the new process, material is now $10/unit. Overhead is charged at 1.6 times direct labor cost. Finished units sell for $31 each. Compute single factor productivity of labor in the old system. Compute it in four possible ways. Compute all factor productivity for both old and new systems. Factor Old System New System Output 60 60(1.25) = 75 # of workers 5 6 Worker cost $12/hr $12/hr Material $16/unit $10/unit Overhead 1.6(labor cost) 1.6(labor cost) Price 31 31

Problem 2; An additional computation Factor Old System New System Output 60 75 # of workers 5 6 Worker cost $12/hr $12/hr Material $16/unit $10/unit Overhead 1.6(labor cost) 1.6(labor cost) Price 31 31 Compute labor productivity for the old system Labor Productivity = 60/5 = 12 units per worker Labor Productivity = [(60)(31)]/5 = 372 $ per worker Labor Productivity = 60/[(5)(12)] = 1 unit per dollar Labor Productivity = [(60)(31)]/[(5)(12)] = 31

Problem 2; AFP Factor Old System New System Output 60 75 # of workers 5 6 Worker cost $12/hr $12/hr Material $16/unit $10/unit Overhead 1.6(labor cost) 1.6(labor cost) Price 31 31 Since there is only a single output, in the nominator we can have either # or $. Since it is all factor productivity, in the denominator we must have $

Problem 2; AFP Old System Factor Old System New System Output 60 75 # of workers 5 6 Worker cost $12/hr $12/hr Material $16/unit $10/unit Overhead 1.6(labor cost) 1.6(labor cost) Price 31 31 Old System Denominator of all factor productivity is computed as (5)(12) + (16)(60) + (1.6) (5)(12) = 1116 We could have either 60 (number) or (60)(31) = 1860 (dollar) in the nominator All factor productivity for old system = 60/1116 = .054 unit/$ All factor productivity for old system = 1860/1116 = 1.67

Problem 2; AFP New System Factor Old System New System Output 60 75 # of workers 5 6 Worker cost $12/hr $12/hr Material $16/unit $10/unit Overhead 1.6(labor cost) 1.6(labor cost) Price 31 31 New System 75 / [(6)(12) + (10)(75) + (1.6) (6)(12)] = .08 unit/$ Or [(75)(31)]/ [(6)(12) + (10)(75) + (1.6) (6)(12)] = 2.48 1.67 in the old system 2.48 in the new system