Suppose that a firm makes gears (G) and axles (A). Each gear requires 0.75 hours of labor and each axle requires 1.25 hours of labor. Six thousand minutes of labor are available. How should the labor constraint(s) be written? 0.75G + 1.25A ≤ 6000 0.75G + 1.25A ≤ 100 0.75G + 1.25A ≥ 6000 45G + 75A ≤ 100 45G + 75A ≤ 1000

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PLEASE USE SIMPLEX METHOD. Thank you! Suppose a company manufactures different electronic components for computers. Component A requires 2 hours of fabrication and an hour of assembly. Component B requires 3 hours of fabrication and an hour of assembly, and component C requires 2 hours of fabrication and 2 hours of assembly. The company has upto 1,000 labor-hours for fabrication, 800 labor-hours of assembly time each work. If the profit on each component A, B, and C is $7, $8, and $10 respectively, how many of each should be produced to maximize profit?

SM manufacturer produces scarves. They evenly split the $600 factory rent with GM gloves manufacturers, and the raw material for each scarf costs $2. If the selling price of a pair of GM gloves is $4 and a SM scarf is $5, how many scarves should SM sell to break even?

Sturgill Manufacturing Inc. needs to predict the numbers of machines and employees required to produce its planned production for the coming year. The plant runs three shifts continuously during the workweek, for a total of 120 hours of capacity per week. The shop efficiency (the percent of total time available for production), which accounts for setups, changeovers, and maintenance, averages 70% with a standard deviation of 5%, which reduces the weekly capacity. Six key parts are produced, and the plant has three different types of machines to produce each part. The machines are not interchangeable as they each have a specific function. The time to produce each part on each machine varies. The mean time and standard deviation (in hours) to produce each part on each machine are shown below: Mean Time Part Type Machine A Machine B Machine C 1 3.5 2.6     8.9 2 3.4 2.5  8 3 1.8 3.5 12.6 4 2.4 5.8 12.5 5 4.2 4.3 28  6…

JCL Inc. is a major chip manufacturing firm that sells its products to computer manufacturers like Dell, Gateway, and others. In simplified terms, chip making at JCL Inc. involves three basic operations: depositing, patterning, and etching. Depositing: Using chemical vapor deposition (CVD) technology, an insulating material is deposited on the wafer surface, forming a thin layer of solid material on the chip. Patterning: Photolithography projects a microscopic circuit pattern on the wafer surface, which has a light-sensitive chemical like the emulsion on photographic film. It is repeated many times as each layer of the chip is built. Etching: Etching removes selected material from the chip surface to create the device structures.   The table below lists the required processing times and setup times at each of the steps. There is unlimited space for buffer inventory between these steps. Assume that the unit of production is a wafer, from which individual chips are cut at a later…

Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and C. The labor-hour requirements, by department, are as follows. Department Product 1 Product 2 Product 3 A 1.50 3.00 2.00 B 2.00 1.00 2.50 C 0.25 0.25 0.25 During the next production period, the labor-hours available are 450 in department A, 350 in department B, and 50 in department C. The profit contributions per unit are $23 for product 1, $27 for product 2, and $28 for product 3. (a) Formulate a linear programming model for maximizing total profit contribution. (Let P; = units of product i produced, for i = 1, 2, 3.) Max 23P1 +27P2+28P3 s.t. +3P2+2P3≤ 450 Department A 1.5P1 Department B 2P1+1P2 +2.5P3 <350 Department C 0.25P1 +0.25P2+0.25P3 <50 P1, P2, P3 ≥0 (b) Solve the linear program formulated in part (a). How much of each product should be produced, and what is the projected total profit contribution (in dollars)? (P1, P2, P3) = 60,80,60 with profit $ 5220 (c)…

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