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Joy and Kim have normal 9-5 jobs during the week. On the weekends, they have a side hustle where they make wooden toys and sell them on Etsy. Joy does the woodwork, and then Kim paints the toys. Joy can work at most 4 hours over the weekend, and Kim can work at most 6 hours over the weekend. Production data is below. Toy Name Material Cost Selling Price Woodwork time Paint time Car $2/toy $9/toy 5 minutes/toy 4 minutes/toy Soldier $2/toy $11/toy 5 minutes/toy 8 minutes/toy Train $3/toy $13/toy 5 minutes/toy 6 minutes/toy Joy and Kim are trying to determine what to produce on an average weekend to maximize their profit. Formulate a linear program for this problem. Clearly define your decision variables and any indices/parameters that you use. Also, be sure to write out your objective function and constraints “in words” and “in math”. Do not solve the LP.

Please answer these problems with solutions neatly, accurately, and with necessary drawings/figures. Kindly encode everything, if possible. ANCHORED SHEET PILES PROBLEM 1 An anchored sheet pile wall is to be constructed to support an excavation 8 meters deep in a multi-layered soil system. The top 4 meters is a granular backfill with a unit weight of 19 kN/m3 and a friction angle of 34°. The lower layer is a submerged sand with a saturated unit weight of 21 kN/m3 and a friction angle of 30°. The anchor is located 1.5 meters below the ground surface. Using the Free Earth Support method, compute the required depth of embedment and the tension in the anchor bolt per unit length of the wall. PROBLEM 2 An 8-meter-deep excavation is supported by an anchored sheet pile wall in a cohesive soil. The soil has a unit weight of 19.5 kN/m3 and a cohesion of 35 kPa. The anchor is located at a depth of 1.2 meters. Using the Fixed Earth Support method, determine the minimum length of the sheet pile for equilibrium and the tension in the anchor bolt. PROBLEM 3 A 10-meter-high anchored sheet pile wall retains a cohesionless soil with a unit weight of 18.8 kN/m3 and a friction angle of 33°. The anchor bolts are placed 1.8 meters below the ground surface. The wall is designed for a safety factor of 1.5 against pullout. Calculate the required tension in each anchor bolt if the spacing between them is 2 meters and 4 meters, and analyze the effect of increased spacing. PROBLEM 4 An anchored sheet pile wall is installed in a soil with a unit weight of 19.2 kN/m3 and a friction angle of 29°. The excavation depth is 7 meters. A uniform surcharge of 10 kN/m2 is applied to the backfill. The water table is located 2 meters below the ground surface on the retained side and at the dredge line on the excavated side. The anchor is placed 1.5 meters below the ground surface. Using either the Free Earth Support or Fixed Earth Support method, determine the required depth of embedment and the tension in the anchor.

Nuria y Cristina ser/estar (1) (nuevo)estudiantes (2) (universitario). La universidad ser/estar (3) (grande) y está en Athens, Ohio. Nuria y Cristina ser/estar de Bogotá, Colombia, y no conocían Estados Unidos (they had never been to the US before). Las dos ser/estar estudiantes de periodismo muy (4) (dedicado). El Departamento de

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Ex 4.1 the Knudsen number which plays an important role in low density flow problem, is defined as the dimensionless ratio a/l where a is the mean free path and l is some characteristic length of the boundaries. Flow for which a/l greater than or equal to 1 is sometime called free molecule flow. Consider a sphere 1 foot

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