Question

It costs a company $125.67 to manufacture a dishwasher appliance and $345.67 to manufacture a refrigerator. Each dishwasher requires 4 workers and each refrigerator requires 8 workers. Only 36 workers are available each day. Each dishwasher requires 3.6 hours to build and each refrigerator requires 8.7 hours to build. At least 67.8 hours per day are available for building the appliances. Each dishwasher requires 4.2 hours for testing and each refrigerator requires 3.4 hours for testing. At least 56.8 testing hours are available per day. Each dishwasher requires 2 hours for packaging and each refrigerator requires 3 hours for packaging. At least 46 hours per day are available for packaging. How many dishwashers and refrigerators should the company manufacture per day in order to minimize the production costs? Use those results to find the minimum cost per day.

		$1,289.35
		$1,308.66
		$1,391.15
		$1,412.86
		There is no feasible region. Since all constraints cannot be satisfied at the same time, this problem has no solution.

Answer 1

Answer : Last Option No feasible solution.

Details

Let x and y respectively represent the number of dishwasher and refrigerator to be produced. Then. The LPP is:

Minimize Z = 126.57x + 345.67y

Subject to

4x + 8y ≤ 36 [worker constraint]

3.6x + 8.7y ≥ 67.8 [building hours per day constraint]

4.2x + 3.4y ≥ 56.8 [testing hours per day constraint]

2x + 3y ≥ 46 [packaging hours per day constraint]

x, y ≥ 0.

Graphing the above constraints we find that there are no points in the first quadrant that satisfy the first two constraints simultaneously. Thus, there is no feasible region.

DONE