Solve for the quantities of x and y which will maximize Z. The x = The y = What

Question

Solve for the quantities of x and y which will maximize Z. The x = The y = What is the maximum value of Z? The Z = A company that makes shopping carts for supermarkets and other stores recently purchased some new equipment that reduces the labor content of the jobs needed to produce the shopping carts. Prior to buying the new equipment, the company used 6 workers, who produced an average of $1 carts per hour. Workers receives $12 per hour, and machine coast was $39 per hour. With the new equipment, it was possible to transfer one of the workers to another department, and equipment cost increased by $18 per hour while output increased by four carts per hour. Compute the multifactor productivity (MFP) (labor plus equipment) under the After buying the new equipment. The MFO (carts/$) = Compute the % growth in productivity between the Prior to and after buying the new equipment. The growth is productivity = % (round to 2 decimal places) Given is a CPM project network diagram as shown below.

Explanation / Answer

Old Case:

Number of workers = 6

Cost per worker = $12 per hour

Machine cost = $ 39 per hour

Output = 81 units per hour

MFPold = 81/(6*12 + 39)

MFPold = 0.7297

Improved case

Number of workers = 5

Cost per worker = $12 per hour

Machine cost = $ 57 per hour

Output = 85 units per hour

MFPnew = 85/(5*12 + 57)

MFPnew = 0.7264

Zero % change in productivity

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