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You work for the Sawzall Company which manufactures two types of sawzalls: a corded model and a cordless model. You have contracted to supply a national retail chain with a total of 30,000 corded sawzalls and 15,000 cordless sawzalls. However, Sawzall’s production capability is limited in three departments: production, assembly, and packaging. The following table summarizes the hours of processing time available and the processing time required by each department, for both types of sawzalls:
| Hours Required Per Sawzall | |||
| Department | Corded | Cordless | Hours Available |
| Production | 0.2 | 0.4 | 10,000 |
| Assembly | 0.3 | 0.5 | 15,000 |
| Packaging | 0.1 | 0.1 | 5,000 |
The company makes its corded sawzall in-house for $55 and its cordless sawzall for $85. Alternatively, it can buy corded and cordless sawzalls from another source for $67 and $95, respectively. How many cordless and corded saws should Sawzall make and how many should it buy from its competitor in order to fulfill its contract in the least costly manner?
Formulate this problem as a LP
Solve this problem using Solver
Expert Answer
Let the production of corded and cordless models be a and b respecrively and let the outsurcing of corded and cordless model be c and d respectively.
Objective function:
Minimize z= 55a+85b+67c+95d
Subjected to:
0.2a+0.4b <= 10000 (production hours constraints)
0.3a+0.5b <= 15000 (assembly hours constraints)
0.1(a+b) < = 5000 (packaging hours constraint)
a+c = 30000 (contract constraint for corded)
b+d = 15000 (contract constraint for cordless)
a,b,c,d >= 0 (non-negativity constraint)
The same has been solved using Excel Solver, the result of which is shown below along with solver parameters:
