Make or Buy A sudden increase in the demand for smoke detect

Make or Buy. A sudden increase in the demand for smoke detectors has left Acme Alarms with insufficient capacity to meet demand. The company has seen monthly demand from its retailers for its electronic and battery-operated detectors rise to 20,000 and 10,000 respectively. Acme’s production process involves three departments: fabrication, assembly, and shipping. The relevant quantitative data on production and prices are summarized as follows:

Monthly Hours Available

Hours/Unit

(Electronic)

Hours/Unit (Battery)

Fabrication

2,000

0.15

0.10

Assembly

4,200

0.20

0.20

Shipping

2,500

0.10

0.15

Determine the optimal leasing schedule. What is the optimal total cost and the corresponding schedule?

Solution

let the numer of electronic detectors produced be \"x\" and battery detectors be \"y\"

so, x=20,000 and y=10,000 (demand)

subject to constraints:

0.15x+0.10y<=2,000 (fabrication)

0.20x+0.20y<=4200 (assembly)

0.10x+0.15y<=2500 (shipping)

Solving the linear program using solver in excel, we get the following solution:

shipping

Thus given the constraints of monthly hours, 6,666.67 units of electronic and 10,000 units of battery detectors can be produced.

optimal cost cannot be determined as no cost details are given.