Old MathJax webview 1. The Otto Maddick Machine Tool Company produces two products, muffler…

Old MathJax webview

1. The Otto Maddick Machine Tool Company produces two products, muffler bearings and torque amplifiers. One muffler bearing requires 0.125 hours of assembly labor, 0.25 hours in the stamping department and 9 square feet of sheet metal. Each torque amplifier requires 1/3 hours in assembly and 0.25 hours in stamping and uses 6 square feet of sheet metal. Current capacities are 400 hours of assembly labor and 375 hours of stamping capacity. Sheet steel costs $0.15 per square foot. Muffler bearings sell for $9 and torque amplifiers sell for $11.00. Use linear optimization to find the number of each product to make to maximize profit. Do not constrain the solution to integers. The available amount of sheet steel may be considered unlimited. The cost of Labor is not charged to the products.
A new product called the furtengrinder uses 0.5 hours of assembly time and 10 square feet of sheet metal and sells for $32.10.
Use shadow prices from Solver’s sensitivity report to determine the maximum number of stamping hours it could use before it would become unprofitable to produce furtengrinders.
Answer: cost impacting the profitability of the product is the steel sheet (sq feet). However, the total number of products that can be made is limited by the available capacities of labour and stamping department hours.
Let M, T and F denote the number of Muffler bearings, Torque amplifiers and Furtengrinder
Profitability of
Muffler bearings = Price – steel sheet*cost per sq ft = 9 – (9*0.15) = $7.65
Torque amplifiers = 11 – (6*0.15) = $10.1
Furtengrinder = 32.1 – (10*0.15) = $30.6
Objective function
Maximize 7.65*M + 10.1*T +…

2. A post office requires sufficient full- and part-time staff to satisfy the following daily needs for employee hours:
Day M T W R F Sa Su
Hours Needed 136 104 120 152 112 128 88

A full-time employee works 8 hours a day for five straight days. A part-time employee works 4 hours a day for five straight days. Full- or part-time employees can be hired to begin their five straight days on any day that the post office chooses. Full time employees earn $20/ hour while part time employees earn $15/hour. A union agreement limits the number of part-time employees to no more than 25% of the total number of employees. Determine how many full- and part-time workers should begin their work on each day of the week to satisfy the manpower requirements at minimum cost. Ignore lunch and other breaks.

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