In the market place, there is competition for raw materials or the inputs to production. This...

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In the market place, there is competition for raw materials or the inputs to production. This collective competition is the hidden hand that sets the price for goods in the market place, in this case the resin and the workers' labor. The goal of the market is to make the most money possible from its resources by setting the highest prices possible for them, but it does not want to put the producers out of business: it just wants to take all of their profit. Let y1 be the price increase for a pound of resin and y2 be the price increase for an hour of labor, where y1,y2 >0. (a) By how much will the cost of producing one case of beer mugs increase? Similarly, by how much will the cost of producing one case of champagne glasses increase? (b) Write two inequalities that represent that the market wants to set the prices so that it takes the profits made on the business producing beer mugs and champagne glasses. (c) By minimizing the total increase in the cost of raw materials subject to wiping out the producer's profit, we should keep the Plastic Cup Factory in business. Write and solve this linear program. (d) The answer to part (c) should look familiar. Can you explain why that is? In the market place, there is competition for raw materials or the inputs to production. This collective competition is the hidden hand that sets the price for goods in the market place, in this case the resin and the workers' labor. The goal of the market is to make the most money possible from its resources by setting the highest prices possible for them, but it does not want to put the producers out of business: it just wants to take all of their profit. Let y1 be the price increase for a pound of resin and y2 be the price increase for an hour of labor, where y1,y2 >0. (a) By how much will the cost of producing one case of beer mugs increase? Similarly, by how much will the cost of producing one case of champagne glasses increase? (b) Write two inequalities that represent that the market wants to set the prices so that it takes the profits made on the business producing beer mugs and champagne glasses. (c) By minimizing the total increase in the cost of raw materials subject to wiping out the producer's profit, we should keep the Plastic Cup Factory in business. Write and solve this linear program. (d) The answer to part (c) should look familiar. Can you explain why that is?