Sleep-Easy Waterbeds Limited manufactures two nicely finished models of bed frames, the Contemporary and the Colonial. The
Question:
Sleep-Easy Waterbeds Limited manufactures two nicely finished models of bed frames, the Contemporary and the Colonial. The gross profit is $85 for the Contemporary model and $125 for the Colonial model. Both products must go through three distinct job-shop processes for cutting, assembling, and final finishing. The shops are also used for other small products, but are exclusively available for the two models of bed frames for a maximum of 300, 210, and 336 man-hours per week, respectively. The Colonial and the Contemporary bed frames require the following job-shop time, in man-hours:
| Job-shop | Contemporary | Colonial |
| Cutting | 3 | 2 |
| Assembling | 1.5 | 3 |
| Final Finishing | 3 | 4 |
The marketing department has stipulated that not more than seventy (70) Contemporary models should be produced each week. Also, at least twenty (20) Colonial models must be produced weekly. Sleep-Easy Waterbeds Limited wishes to maximize its weekly gross profits.
Variables defined:
X1(Cn) = Number of Contemporary models to produce.
X2(Cl) = Number of Colonial models to produce.
Objective Function: MAXIMIZE: Z = 85X1+ 125X2
Constraints:
3X1+ 2X2<=300 (Cutting)
1.5X1+ 3X2<=210 (Assembling)
3X1+ 4X2<=336 (Final Finishing)
1X1<=70 (Contemporary Limit)
1X2>=20 (Colonial Minimum)
And1X1, 1X2>=0 (Nonnegativity)
Expert Answer:
