Question

Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited, so at most 8 will be produced.a. Formulate the LP model for this problem. b. Solve the problem using the graphical method.

Answer 1

Explanation:

To  formulate the LP model for this problem,

Let,

X1 = Number of beds to produce

X2 = Number of Desks to produce

Our objective function:

Max: 30X1 + 40X2

Constraints:

• 6X1 + 4X2 ≤ 36 available carpentry hours
• 4X1 + 8X2 ≤ 40 available vanishing hours
• X2 ≤ 8 (demand for X2)
• X1, X2 ≥0

Based on the constraints information as well as the objective function you can then solve using the graphical method.