0.a) In DJJ Enterprises manufactures, two of these automotive parts are camshaft
ID: 2470391 • Letter: 0
Question
0.a) In DJJ Enterprises manufactures, two of these automotive parts are camshafts and gears. Camshafts earn a profit of $25 per unit and gears earn $18 per unit. Three major resources are utilized in the production process: steel, labor, and machine time. It takes 5 lbs of steel to make a camshaft, and 8 lbs to make a gear. Camshafts require 1 hour of labor; gears require 4 hours. It takes 3 hours machine time per camshaft, and 2 hours per gear. For the current planning period, 5000 lbs steel, 1500 hours labor, and 1000 hours machine time are available. DJJ would like to maximize profit during the current planning period, within allowable resources. b) Consider the following table providing nutritional and cost data in a restaurant that you suppose to have breakfast and lunch there. To find a reasonably nutritious diet that minimizes sodium intake, you have determined that the nutrition requirements indicate that the diet must contain 2000-2500 calories, have no more than 85 grams of fat, and contain at least 100% of the "daily value" (DV) of Vitamin C, Vitamin A, Calcium, and Iron. If you has $15 budgeted for the two meals combined. If you are willing to eat no more than two of each item from the menu, develop an algebraic formulation to minimize sodium intake.
Larger Burger
Larger Burger
Small burger Chicken strips Chili Deluxe Salads Side Salad Baked Potato FrenchFries Milk Shake Cost $2.20 $0.99 $2.30 $0.99 $1.95 $0.99 $1.75 $1.50 $0.79 $1.50 Calories 410 270 410 200 410 140 390 400 120 330 Total Fat(g) 19 9 18 5 32 8 12 17 4.5 8 Vitamin C%DV 10 0 0 4 60 30 60 6 0 0 Vitamin A %DV 6 0 0 15 170 140 15 2 10 15 Cacium %DV 6 4 0 8 35 8 8 0 25 30 Iron %DV 25 20 6 10 20 6 15 8 0 15 Sodium (mg) 910 630 1470 870 840 570 160 340 120 150Explanation / Answer
Objective: Maximize the profit
Z=$25C+$18G (C=Camshafts and G=Gears)
Subject to the Constraint:
1x1+4X2<1500
3x1+2x2<1,000
5x1+8x2<5,000
x1,x2>0
__________________________________________________________________________
b)Objective=Minimize the sodium
X=910x1+630x2+1470x3+870x4+840x5+570x6+160x7+340x8+120x9+150x10
Subject to the constraints
410x1+270x2+410x3+200x4+410x5+140x6+390x7 +400x8+120x9+330x10>2000
410x1+270x2+410x3+200x4+410x5+140x6+390x7 +400x8+120x9+330x10<2500
19x1+9x2+18x3+5x4+32x5+8x6+12x7+17x8+4.5x9+8x10<85
10x1+0x2+0x3+4x4+60x5+30x6+60x7+6x8+0x9+0x10>100
6x1+0x2+0x3+15x4+170x5+140x6+15x7+2x8+10x9+15x10>100
6x1+4x2+0x3+8x4+35x5+ 8x6+8x7+0x8+25x9+30x10>100
25x1+20x2+6x3+10x4+20x5+6x6+15x7+8x8+0x9+15x10>100
2.20x1+0.99x2+2.30x3+0.99x4+1.95x5+0.99x6+1.75x7+1.50x8+0.79x9+1.50x10<15
x1,x2,x3,x4,x5,x6,x7,x8,x9,x10<0
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.