do test only use techniqes found in files
Answer Report 1
| Microsoft Excel 16.0 Answer Report | ||||||
| Worksheet: [LP basic.xlsx]Basic LP | ||||||
| Report Created: 8/13/2025 4:50:54 PM | ||||||
| Result: Solver found a solution. All Constraints and optimality conditions are satisfied. | ||||||
| Solver Engine | ||||||
| Engine: Simplex LP | ||||||
| Solution Time: 6.11 Seconds. | ||||||
| Iterations: 1 Subproblems: 2 | ||||||
| Solver Options | ||||||
| Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Show Iteration Results | ||||||
| Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative | ||||||
| Objective Cell (Max) | ||||||
| Cell | Name | Original Value | Final Value | |||
| $K$4 | max obj | 64 | 64 | |||
| Variable Cells | ||||||
| Cell | Name | Original Value | Final Value | Integer | ||
| $G$3 | A | 6 | 6 | Integer | ||
| $H$3 | B | 2 | 2 | Integer | ||
| $I$3 | C | 4 | 4 | Integer | ||
| Constraints | ||||||
| Cell | Name | Cell Value | Formula | Status | Slack | |
| $K$6 | LHS | 20 | $K$6<=$M$6 | Binding | 0 | |
| $K$7 | LHS | 2 | $K$7>=$M$7 | Binding | 0 | |
| $K$8 | LHS | 14 | $K$8<=$M$8 | Not Binding | 1 | |
| $G$3:$I$3=Integer |
Basic LP
| A | B | C | ||||||||||
| 6 | 2 | 4 | ||||||||||
| max obj | 5 | -3 | 10 | 64 | ||||||||
| LHS | type | RHS | ||||||||||
| 1 | 1 | 3 | 20 | <= | 20 | |||||||
| 1 | 2 | >= | 2 | |||||||||
| 3 | -2 | 14 | <= | 15 |
Maximize 5A -3B +10C subject to: A + B + 3C <= 20 B >= 2 3A - 2B <= 15 A,B,C >= 0
Sheds
A small firm builds three types of garden sheds. Type A requires 2 hours of machine time and 5 hours of craftsman time. Type B requires 3 hours of machine time and 5 hours of craftsman time. Type C requires 4 hours of machine time and 3 hours of craftsman time. Each day there are 200 hours of machine time available and 160 hours of craftsman time. The profit on each type A shed is $80, on each type B shed is $84, and on each type C shed is 85 . How many sheds of each type should we make to maximize the profit?