[Excel spreadsheet available at http://web.mit.edu/15.053/www/Exer3.15.xls] The Concrete Products…
[Excel spreadsheet available at http://web.mit.edu/15.053/www/Exer3.15.xls] The Concrete Products Corporation has the capability of producing four types of concrete blocks. Each block must be subjected to four processes: batch mixing, mold vibrating, inspection, and yard drying. The plant manager desires to maximize profits during the next month. During the upcoming thirty days, he has 800 machine hours available on the batch mixer, 1000 hours on the mold vibrator, and 340 man-hours of inspection time. Yard-drying time is unconstrained. The production director has formulated his problem as a linear program with the following initial tableau:
a) By how much must the profit on a pallet of number 3 blocks be increased before it would be profitable to manufacture them?
b) What minimum profit on x2 must be realized so that it remains in the production schedule?
c) If the 800 machine-hours capacity on the batch mixer is uncertain, for what range of machine hours will it remain feasible to produce blocks 1 and 2?
d) A competitor located next door has offered the manager additional batch-mixing time at a rate of $4.00 per hour. Should he accept this offer?
e) The owner has approached the manager with a thought about producing a new type of concrete block that would require 4 hours of batch mixing, 4 hours of molding, and 1 hour of inspection per pallet. What should be the profit per pallet if block number 5 is to be included in the optimal schedule?