BoWw N e A B Cc D E F G H 1 1 K Afarmer owns 500 hectares of land in an arid region. The government gives him up to 1,000,000 cubic metres of water for irrigation each year. In addition, he may purchase up to an additional 800,000 cubic metres of water per annum at a cost of $0.20 per cubic metre. He grows corn, peas, and onions. The net revenue per hectare of each commodity (excluding the cost of purchased water, if any) and the water requirement in cubic metres per hectare are shown in the table. He wishes to diversify his crop in case one commodity suffers an unanticipated fall in price. Therefore, no commoedity may occupy more than 50% of the total area planted, nor may any commadity occupy less than 10% of the total area planted. 1) Find the optimal solution using excel Solver. 2) Describe your findings: objective value, optimal solution, and constraint observations. 3) Remember all constraints must be in standard form. M N o Revenue Water Requirement Commodity per Hectare (cubic metres per hectare) Corn 4000 Peas 6000 Onions 2000 Free Available 1000000 Purchase Available 800000 Purchase cost/ m Tilland (hectares) 500 Min land / crop 10% Max land / crop 50% O @ - @ e B N RORR N R R e e e e e W N D W00~ oW R W N e o A B c D E F G H | J A metalworking company buys sheet metal from which they make swings and slides for children's playgrounds. They then outsource the rustproofing of the swings and slides, and sell the finished products. They buy the metal at a cost of 5 per kilogram (kg). Each swing requires 3 kg of metal, while each slide requires 6 kg. Each product spends time in three operations: cutting; polishing; and assembly. The times in minutes per unit are in the table. Each day, the shop is available for 6.5 hours of productive time. There are four cutting machines, one polisher, and one person to do the assembly. However, up to an extra 80 minutes of assembly time can be purchased for $2 per minute. The rust-proofing firm charges $30 per hour. When rustproofing swings, they can rust-proof & swings per hour; when rust-proofing slides, they can rust-proof 16 slides per hour. The metalworking company sells its products to a wholesaler at $190 per swing and $75 per slide. The market requires that at least two slides be made for every swing made. We define all variables are on a daily basis as shown. 1) Find the optimal solution using excel Solver. 2) Describe your findings: objective value, optimal solution, and constraint observations. 3) Remember all constraints must be in standard form. 1 Cutting Polishing Assembly Swing 25 12 16 Slide 18 10 11 Xy = the number of swings made (integer) X, = the number of slides made (integer) X3 = the number of hours of rust-proofing purchased X; = the number of kilograms of metal purchased X5 = the number of extra assembly minutes purchased A B Cc D E F G H | ] M N o 3 v w X Y The production manager of a company needs to determine next month's production plan for the company's ten products. Each product is measured in units (an integer) per month. The products use six resources: assembly line 1; assembly line 2; painting; dryers; packaging; and storage. Each month, the produced units are sent to sterage in the warehouse. At the end of each menth, all contents in storage are sent to the customers. The first five resources are each measured in hours, while storage is measured in cubic metres (m?). The requirements per unit for each product, and the amount of each resource Product 1 2 6 9 10 Available available are shown in the table. Assembly 1 2 0.25 hours Assembly 2 0 0.65 hours i. There should be at most 4,500 units produced. Painting 0 0.2 0.65 hours ii. There should be at least two units of product 3 for every unit of the combined production of products 6 Dryers 0 0.3 0 hours and 8 produced. Packaging 05 0.1 0.65 hours iii. The total production of product 4 should be no more than the combined production of products 2 and 7. Storage 0.25 0.1 0.25 cubic meters iv. The combined production of products 1 and 5 must be at most twice the preduction of product 9. 1) Find the optimal solution using excel Solver. 2) Describe your findings: objective value, optimal solution, and constraint observations. 3) Remember all constraints must be in standard form. Profit/unit $2.10 $3.20 Storage cost $4.30 $5.50 $3.90 A B C D E F G H K L M N O P Q R S T U A car assembly plant produces both sedans and SUV's. The operations at the plant have been algebraically modeled as shown. x1= the number of sedans made each week 12= the number of SUV's made each week 1) Setup the initial tableau using the matrix method as shown in class. Find the entering and exiting variable. 2) Iterate the tableau ONE time. Identify the entering and exiting variable. Maximize 3001 + 400x2 subject to LO CO assembly-line 1 6x1 + 9x2 13500 10 11 assembly-line 2 10x1 + 7x2 14400 12 assembly-line 3 5x1 + 8x2 11700 13 total production 1x1 + 1x2 IA IV IV IA IA IA IN 1800 14 production of sedans 1x1 + 450 15 16 production of SUV's Ox1 + 1x2 630 17 proportion -.65x1 + 0.352 0 18 19 20 21 22 23 24