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| 3. Clarks Place is a store where guitars are sold. Clark and Joe are business partners and guitars at Clarks Place. Gibson and Ibanez are amongst the customers favorite guitars. Clark and Joe want to know how many Gibson and Ibanez guitars they should order to make the most profit. Gibson guitars sell for 5,000$ and Ibanez sell for 2,000$. Both kind of guitars will cost Clark and Joe 1,500$ each. They have a total of 50,000$ to spend on the Ibanez and Gibsons. They want to know how many of each guitar to buy to make the most profit. The variables for this problem are # of gibson and # of Ibanez guitars. You know that they want to order a number or guitars and that number will have to be multiplied by the cost of the guitars. So the variables would have to be, I = # of Ibanez Guitars and G= # of Gibson guitars There is only one constraint in this problem it is the amount of money they have to spend on the guitars. 2,00I + 5000G < 50,000 4. To find the feasible region look back at your constraints while graphing and if it shows a > you shade above the line you graphed and it it's < You shade below the line you graphed. When done shading look at the graph and find where all the colors come together in one certain are, that will be the feasible area for your problem. If a point is on a boundary line of the feasible region is is one of the highest or lowest points for a possible profit or cost line. I made up some constraints I could graph to show the feasible region. a+b < 12 2a+6b > 30 4a+ 2b > 16 a+b <12 If A = 0 b = 12 If B= 0 a = 12 0,12 and 12, 0 ( shade below line) 2a+6b > 30 If a = 0 6b= 30 6 6 b = 5 If b = 0 2a = 30 2 2 a =15 0,5 and 15, 0 (shade above line) 4a+ 2b > 16 If a = 0 2b = 16 2 2 b = 8 If b = 0 4a = 16 4 4 a = 4 0, 8 and 4, 0 (Shade above line) Where the colors green red and yellow meet and are all together in one area is the feasible region. There all the coordinates are either below or above the contraint regions. 3 a + 5 b > 30 if a = 0 5b = 30 5 5 b = 6 if b = 0 3a = 30 3 3 a = 10 0,6 and 10, 0 ( Graph above the line ) 10a + 2b < 50 If a = 0 2 b = 50 2 2 b = 25 if b = 0 10a = 50 10 10 a = 5 0, 25 and 5, 0 ( Graph below the line) Where the aqua and blue meet is the feasible region, the arrow points right to it. |
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