Question

Sundown LLC makes patio heating lamps. Their factory in Topeka has 800 in stock, the factory in Dallas has 700, while the warehouse in Memphis needs 500, and the warehouse in Austin needs 650. It costs $12 to ship each lamp from Topeka to Memphis, $20 for Topeka to Austin, $15 from Dallas to Memphis, and $22 from Dallas to Austin. What is the most economical way to minimize its shipping costs and meet the demands of the two warehouses

Answer 1

500T1 + 300T2 + 350D2 = $19,700

• 500 units shipped from Topeka to Memphis
• 300 units shipped from Topeka to Austin
• 350 units shipped from Dallas to Austin

Step-by-step explanation:

minimize the following equation:

12T1 + 20T2 + 15D1 + 22D2

where:

T1 = lamp sent from Topeka to Memphis

T2 = lamp sent from Topeka to Austin

D1 = lamp sent from Dallas to Memphis

D2 = lamp sent from Dallas to Austin

T1 + D1 = 500

T2 + D2 = 650

T1 + T2 ≤ 800

D1 + D2 ≤ 700

using solver, the optimal solution is: 500T1 + 300T2 + 350D2 = $19,700