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Problem: 5-17

Posted on July 28, 2021 by Abigail Stason

Given: In order to keep to a construction schedule, I must place 1000 tons of pavement a day. Because of other projects in the area, I will be unable to purchase all of my pavement from one batch plant. In fact, I will have to purchase from three plants in the area because of the high demand.

Plant G can supply me with up to 275 tons/day, total, of either Topping or Binder – my choice. Thus you can get up to 275 tons of whatever you want – 275 tons of Topping and no Binder, or 100 tons of Topping and 175 tons of Binder, or 2 tons of Topping and 273 tons of Binder, or 10 tons of Topping and no Binder – anything you like, but no more than 275 tons per day.

Plant H can supply up to 350 tons/day of either Topping or Binder, same idea as for Plant G.
Plant I can supply me with up to 595 tons/day of either Topping or Binder, same idea as for Plant G.

I have two pavers, one laying Topping and one laying Binder. The Topping Paver lays 575 tons/day and the Binding Paver lays 425 tons/day, which as you might imagine is the exact daily amount required to construct the road.

The cost to transport paving material from Plant G to the Topping Paver is $32/ton. Cost from Plant G to the Binder Paver is $36/ton, from Plant H to Topping Paver, $30/ton, from Plant H to Binder paver, $33/ton, I to Topping paver, $31/ton and I to Binder paver, $35/ton.

Required: Solve for the minimum cost of acquiring the necessary material.

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