question 24

Formulate an Lamodel for this problem Sketch the feasible rexion for this problem Find the optimal solution 21. Zippy motorcycle manufacturing produce two popular pocket bikes miniature manufacturer wants to produce up to 700 bikes and wants to the number of Raron produced does not exceed the number of Zoomers by more than 100. Tach Razor produced and sold results in a profit of So while each Zoomer results in a proti of $40. The bikes are identical mechanically and only ditfer in the appearance of the polymer-based trim around the fuel tank and Each Razor's trium requires 2 pounds of polymer and 3 hours of production time while each Zoomer requires pound of 2.400 labor hours are available for production of these terms in the coming week a Formulate an LP model for this problem b. Sketch the feasible region for this problem. What is the optimal solution? 22. The Quality Desk Company makes two types of computer desks from laminated particle board. The Presidential model sells for $149 and requires 30 square feet of Senator model sells for $135 and requires 24 square feet of particleboard, 1 keyboard sliding mechanism, and 3 hours of labor to fabricate in the coming week, the com pany can buy up to 15,000 square feet of particle board at a price of S1 35 per square views manufacturing labor as a fixed cost and has 3,000 labor hours available in the coming week for the fabrication of these desks. a. Formulate an LP model for this problem b. Sketch the feasible region for this problem. What is the optimal solution? 23. A farmer in Georgia has a 100-acre farm on which to plant watermelons and canta- loupes. Every acre planted with watermelons requires 50 gallons of water per day and must be prepared for planting with 20 pounds of fertilizer. Every acre planted with cantaloupes requires 75 gallons of water per day and must be prepared for planting with 15 pounds of fertilizer. The farmer estimates that it will take 2 hours of labor to harvest each acre planted with watermelons and 25 hours to harvest each acre planted with cantaloupes. He believes that watermelons will sell for about 53 each, and cantaloupes will sell for about si each. Every acre planted with water melons is expected to yield 90 salable units. Every acre planted with cantaloupes is expected to yield 300 salable units. The farmer can pump about 6,000 gallons of water per day for irrigation purposes from a shallow well. He can buy as much fertilizer as he needs at a cost of $10 per 50-pound bag. Finally, the farmer can hire laborers to harvest the fields at a rate of $5 per hour. If the farmer sells all the watermelons and cantaloupes he produces, how many acres of each crop should the farmer plant in order to maximize profits? a. Formulate an LP model for this problem. b. Sketch the feasible region for this model. c. Find the optimal solution to the problem using level curves. 24. Sanderson Manufacturing produces orate, decorative wood frame doors and win- dows. Each item produced goes through three manufacturing processes. cutting, sanding, and finishing. Each door produced requires 1 hour in cutting, 30 minutes in sanding, and 30 minutes in finishing. Each window requires 30 minutes in cutting. 45 minutes in sanding, and 1 hour in finishing. In the coming week, Sanderson has Introduction to Optimization and Chapter 2 finishing capacity. Assume all doors produced can be sold for a profit of $500, and 40 hours of cutting capacity available, 40 hours of sanding capacity, and 60 hours windows can be sold for a profit of $400. Formulate an LP model for this problem. b. Sketch the feasible region. What is the optimal solution? 25. PC-Express is a computer retail store that sells desktops and laptops. The company at $600 on each desktop computer it sells and $900 on each laptop. The computers PC 75 laptops to PC-Express next month. The employees at PC-Express must spend alocsa Express sells are actually manufactured by another company. This manufacturer 2 hours installing software and checking each desktop computer the company wel a special order to fill for another customer and cannot ship more than 80 desktops expects to have about 300 hours available for this purpose during the next month. The They spend roughly 3 hours to complete this process for laptop computers. PC-EXPRE are unsure how many desktops and laptops they should order to maximize profits. store's management is fairly certain that they can sell all the computers they order a. Formulate an LP model for this problem. b. Sketch the feasible region for this model. American Auto is evaluating its marketing plan for the sedans, SUVs, and trucks the c. Find the optimal solution to the problem by enumerating the corner points. estimates each showing of this commercial will cost $500,000 and increase sales company produces. A TV ad featuring this SUV has been developed. The compar SUVs by 3% but reduce sales of trucks by 1% and have no effect on the sales of Cans. The company also has a print ad campaign developed that it can run in vari ach magazine title the ad runs in will increase the sales of sedans, SUVs, and try ationally distributed magazines at a cost of $750,000 per title. It is estimated - 2%, 1%, and 4%, respectively. The company desires to increase sales of sed mar Vs, and trucks by at least 3%, 14%, and 4%, respectively, in the least costly Formulate an LP model for this problem. Sketch the feasible region. What is the optimal solution? the Lines They Are a-Changin' h apologies to Bob Dylan) your assistance er of Blue Ridge Hot Tubs, Howie Jones, has asked for Ehe feasible region and solution to his production problem might ch ammoters in the LP model. He is hoping th= Formulate an Lamodel for this problem Sketch the feasible rexion for this problem Find the optimal solution 21. Zippy motorcycle manufacturing produce two popular pocket bikes miniature manufacturer wants to produce up to 700 bikes and wants to the number of Raron produced does not exceed the number of Zoomers by more than 100. Tach Razor produced and sold results in a profit of So while each Zoomer results in a proti of $40. The bikes are identical mechanically and only ditfer in the appearance of the polymer-based trim around the fuel tank and Each Razor's trium requires 2 pounds of polymer and 3 hours of production time while each Zoomer requires pound of 2.400 labor hours are available for production of these terms in the coming week a Formulate an LP model for this problem b. Sketch the feasible region for this problem. What is the optimal solution? 22. The Quality Desk Company makes two types of computer desks from laminated particle board. The Presidential model sells for $149 and requires 30 square feet of Senator model sells for $135 and requires 24 square feet of particleboard, 1 keyboard sliding mechanism, and 3 hours of labor to fabricate in the coming week, the com pany can buy up to 15,000 square feet of particle board at a price of S1 35 per square views manufacturing labor as a fixed cost and has 3,000 labor hours available in the coming week for the fabrication of these desks. a. Formulate an LP model for this problem b. Sketch the feasible region for this problem. What is the optimal solution? 23. A farmer in Georgia has a 100-acre farm on which to plant watermelons and canta- loupes. Every acre planted with watermelons requires 50 gallons of water per day and must be prepared for planting with 20 pounds of fertilizer. Every acre planted with cantaloupes requires 75 gallons of water per day and must be prepared for planting with 15 pounds of fertilizer. The farmer estimates that it will take 2 hours of labor to harvest each acre planted with watermelons and 25 hours to harvest each acre planted with cantaloupes. He believes that watermelons will sell for about 53 each, and cantaloupes will sell for about si each. Every acre planted with water melons is expected to yield 90 salable units. Every acre planted with cantaloupes is expected to yield 300 salable units. The farmer can pump about 6,000 gallons of water per day for irrigation purposes from a shallow well. He can buy as much fertilizer as he needs at a cost of $10 per 50-pound bag. Finally, the farmer can hire laborers to harvest the fields at a rate of $5 per hour. If the farmer sells all the watermelons and cantaloupes he produces, how many acres of each crop should the farmer plant in order to maximize profits? a. Formulate an LP model for this problem. b. Sketch the feasible region for this model. c. Find the optimal solution to the problem using level curves. 24. Sanderson Manufacturing produces orate, decorative wood frame doors and win- dows. Each item produced goes through three manufacturing processes. cutting, sanding, and finishing. Each door produced requires 1 hour in cutting, 30 minutes in sanding, and 30 minutes in finishing. Each window requires 30 minutes in cutting. 45 minutes in sanding, and 1 hour in finishing. In the coming week, Sanderson has Introduction to Optimization and Chapter 2 finishing capacity. Assume all doors produced can be sold for a profit of $500, and 40 hours of cutting capacity available, 40 hours of sanding capacity, and 60 hours windows can be sold for a profit of $400. Formulate an LP model for this problem. b. Sketch the feasible region. What is the optimal solution? 25. PC-Express is a computer retail store that sells desktops and laptops. The company at $600 on each desktop computer it sells and $900 on each laptop. The computers PC 75 laptops to PC-Express next month. The employees at PC-Express must spend alocsa Express sells are actually manufactured by another company. This manufacturer 2 hours installing software and checking each desktop computer the company wel a special order to fill for another customer and cannot ship more than 80 desktops expects to have about 300 hours available for this purpose during the next month. The They spend roughly 3 hours to complete this process for laptop computers. PC-EXPRE are unsure how many desktops and laptops they should order to maximize profits. store's management is fairly certain that they can sell all the computers they order a. Formulate an LP model for this problem. b. Sketch the feasible region for this model. American Auto is evaluating its marketing plan for the sedans, SUVs, and trucks the c. Find the optimal solution to the problem by enumerating the corner points. estimates each showing of this commercial will cost $500,000 and increase sales company produces. A TV ad featuring this SUV has been developed. The compar SUVs by 3% but reduce sales of trucks by 1% and have no effect on the sales of Cans. The company also has a print ad campaign developed that it can run in vari ach magazine title the ad runs in will increase the sales of sedans, SUVs, and try ationally distributed magazines at a cost of $750,000 per title. It is estimated - 2%, 1%, and 4%, respectively. The company desires to increase sales of sed mar Vs, and trucks by at least 3%, 14%, and 4%, respectively, in the least costly Formulate an LP model for this problem. Sketch the feasible region. What is the optimal solution? the Lines They Are a-Changin' h apologies to Bob Dylan) your assistance er of Blue Ridge Hot Tubs, Howie Jones, has asked for Ehe feasible region and solution to his production problem might ch ammoters in the LP model. He is hoping th=