Deutchlander Machine Company (DMC) makes two types of printing presses: a four-color litho and a two-color litho. Demand for both products is booming and exceeds DMC’s ability to satisfy it. Most raw materials are plentiful, but production is limited by three factors: a shortage of steel rollers, gear cutting capacity, and roller polishing capacity. Each four-color press requires 16 rollers, and each two-color press requires 8 rollers. The four-color presses require 30 hours of gear cutting and 8 hours of polishing time, and the two-color presses require 12 hours of gear cutting and 3 hours of polishing time. DMC is able to buy 100 rollers per week, and it has 160 hours of gear cutting time and 40 hours of polishing time available per week. To avoid harming long-term sales, DMC does not want to raise prices. At current prices DMC will earn a profit of 24,000 on each four-color press made and 10,000 on each two-color press made. So as not to abandon either product market, DMC also wants to produce at least two units of each press each week. a. Formulate DMC’s problem as a linear program to maximize its profit.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Deutchlander Machine Company (DMC) makes two types of printing presses: a four-color litho and a two-color litho. Demand for both products is booming and exceeds DMC’s ability to satisfy it. Most raw materials are plentiful, but production is limited by three factors: a shortage of steel rollers, gear cutting capacity, and roller polishing capacity.
Each four-color press requires 16 rollers, and each two-color press requires 8 rollers. The four-color presses require 30 hours of gear cutting and 8 hours of polishing time, and the two-color presses require 12 hours of gear cutting and 3 hours of polishing time. DMC is able to buy 100 rollers per week, and it has 160 hours of gear cutting time and 40 hours of polishing time available per week.
To avoid harming long-term sales, DMC does not want to raise prices. At current prices DMC will earn a profit of 24,000 on each four-color press made and 10,000 on each two-color press made. So as not to abandon either product market, DMC also wants to produce at least two units of each press each week.
a. Formulate DMC’s problem as a linear program to maximize
its profit.
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