Mat 540 Assignment 1

Mat 540 Assignment 1 - Mat 540 Assignment 1 Assignment#1...

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Mat 540 Assignment 1 Assignment #1 Case Problem - Julia's Food Booth ARLA PAYNE AUGUST 23, 2015 Strayer University Course: MAT 540 – Quantitative Methods
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A: Formulation of the LP Model Let: X1 = (Pizza), X2 = (hotdogs), X3 = (barbecue sandwiches) Constraints: Maximum fund available for the purchase = $1500 Constraint: 0.75X1 + 0.45X2+ 0.90(X3) ≤ 1500 Cost: Cost per pizza slice = $6 (get 8 slices) =6/8 = $0.75 Cost for a hotdog = $.45 Cost for a barbecue sandwich = $.90 Oven space: Space available = 3 x 4 x 16 = 192 sq. feet = 192 x 12 x 12 =27648 sq. inches The oven will be refilled before half time- 27648 x 2 = 55296 Space required for pizza = 14 x 14 = 196 sq. inches Space required for pizza slice = 196/ 8 = 24.50 sq. inches Space required for a hotdog =16 Space required for a barbecue sandwich = 25 Constraint: Constraint: 24.50 (X1) + 16 (X2) + 25 (X3) ≤ 55296 Julia can sell at least as many slices of pizza(X1) as hot dogs(x2) and barbecue sandwiches (X3) combined Constraint: X1 ≥ X2 + X3 = X1 - X2 - X3 ≥ 0 Julia can sell at least twice as many hot dogs as barbecue sandwiches When:
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X2/X3 ≥ 2 = X2 ≥2 X3 =X2 - 2 X3 ≥ 0
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