Set up a balanced initial blank chart for the "Sparkle Plenty" problem. There is no need to enter a starting solution. Hint: Some transportation problems may require an extra row and column to balance them. The Sparkle Plenty Problem The Sparkle Plenty Diamond Company has orders from three cities as follows: Kuwait, 3500 karats; Paris, 8000 karats; New York, 7000 karats. Its diamond-cutting centers can produce diamonds in the following quantities: Antwerp, 6,500 karats; Rotterdam, 5,000 karats, New York, 4,500 karats. The shipping costs (in dollars per karat) are given in the following table: From To Kuwait Paris New York Antwerp 90 30 90

Find the total cost of the following shipment of materials: 23 floor boxes listed at $4.00 each, less 15% ; 150 half-inch conduits listed at $0.60 each, less 20% ; 125 convenience outlets listed at $0.79 each, less 10% ; 83 single-pole flush switches listed at $0.45 each, less 30%.

1. Big H hatchery sells 50 Rhode Island Red chicks for $117 + $20.50 for shipping. Litter Cs hatchery sells 75 Rhodel Island Red chicks for $163+25.75 shipping. Compare unit price (including shipping) for the chicks.  2. 2liter sodas are on sale at 3 for $7. You reckon you need 20 of them.  What is the unit price of a 2liter soda? How much will 20 sodas cost at this rate?

1. A microwave oven company has two factories in the east coast and the midwest. It takes 25 hours (including packaging, shipping, etc.) to transport the microwave ovens of each order from the factory on the east coast to the central warehouse, while it takes 20 hours from the factory in the Midwest to the central warehouse. Shipping from the East Coast factory to the central warehouse costs $80 per order, while shipping from the Midwest factory to the central warehouse costs $40. Now there are 1,000 hours available for packaging, shipping, etc., and $3,000 can be used as transportation costs. (a) Try to write a linear inequality system describing this transportation system. (b) Try to draw a graph of the linear inequality system and list the corner points.

4. Gabe's Gadgets has stores in three locations, Flint, Pontiac, and Detroit. The number of Gadgets sold in each location in September and October is given in the following table. Flint Pontiac Detroit Flint Pontiac Detroit September 30,000 45,000 70,000 The total cost, in dollars, at each location in September and October is given in the following table. The selling price of each gadget is $30. October 25,000 42,000 60,000 September 8,000 10,000 16,000 October 4,000 9,000 15,000 a. Write a 3x2 matrix X representing the number of gadgets sold at each location in September and October, and a 3x2 matrix C representing the total cost at each location in September and October. b. Find the matrix R where R=30X and explain the meaning of the entry 12. c. Find the matrix P where P=R-C and explain the meaning of the entry P31 -

2. A company is planning to open a maximum of 11 new stores in Chicago. The stores will be built in one of three sizes: a convenience store (open 24 hrs.), a standard store, and an expanded service store. The convivence store requires $4.1215 million to build and 30 employees to operate. The standard store requires $8.25 million to build and 15 employees to operate. The expanded-services store requires $12.375 million to build and 45 employees to operate. The company can dedicate up to $82.5 million for construction, and 300 employees to staff the stores. On average, the convenience store nets $1.2 million annually, the standard store nets $2 million and the expanded service store nets $2.6 million annually. How many of each store should the company build to maximize revenue? Use excel solver.

1. The Collin Freight Company has an order for three products to be delivered to a destination. Product I requires 10 cubic feet, weighs 10 pounds, and has a value of $100. Product II requires 8 cubic feet, weighs 20 pounds, and has a value of $20. Product III requires 20 cubic feet, weighs 40 pounds, and has a value of $200. If the carrier can carry 6,000 cubic feet, 11,000 pounds, and is insured for $36,900o, how many of each product can be carried? erit enimo Cd a. Identify the variables of the problem using x, y and z. iguA erlt eihW.o Enabiol-esue (woy b. Fill out the following table from the information given: elelganoo eno 18sal te nib moo arlt blucrte tiero y total Volume (cu. ft.) ole afinu USS Weight (lb.) adt lo of bea Value ($) D8.nl teinothtun Ae Exe ebuloni of el telb orTaboot lao lo alinu 0AE Uo vism woHwolod eldst or ni betealbol el abool otefetnemenupen toib orlt toem hours boot c. Write the augmented matrix for the system of equations. l boot bool mulole A nimelV d.…

An automobile company produces cars in Los Angeles and Detroit and has a warehouse in Atlanta.The company supplies cars to customers in Houston and Tampa. The costs of shipping a car betweenvarious points are listed in the table below, where a blank means that a shipment is not allowed. LosAngeles can produce up to 1100 cars, and Detroit can produce up to 2900 cars. Houston must receive2400 cars, and Tampa must receive 1500 cars. (Include your formulations to receive credit. Thinkcarefully about the transhipment locations.) (a) Determine how to minimize the cost of meeting demands in Houston and Tampa. (b) Modify the answer to part (a) if shipments between Los Angeles and Detroit are not allowed.  (c) Modify the answer to part (a) if shipments between Houston and Tampa are allowed at a cost of$5 per car.

11. Suppose you make and sell skin lotion. A quart of regular skin lotion contains 2 c oil and 1 c cocoa butter. A quart of extra-rich skin lotion contains 1 c oil and 2 c cocoa butter. You will make a profit of $10/qt on regular lotion and a profit of $8/qt on extra-rich lotion. You have 24 c oil and 18 c cocoa butter. a. How many quarts of each type of lotion should you make to maximize your profit? b. What is the maximum profit?