## Related questions with answers

Acrosonic of the earlier example also manufactures a model G loudspeaker system in plants I and II. The output at Plant I is at most 800 systems/month whereas the output at Plant II is at most $600 / \mathrm{month}$. These loudspeaker systems are also shipped to three warehouses- $A, B$, and $C$-whose minimum monthly requirements are 500,400 , and 400 , respectively. Shipping costs from Plant I to Warehouse $A$, Warehouse $B$, and Warehouse $C$ are $\$ 16, \$ 20$, and $\$ 22$ per system, respectively, and shipping costs from Plant II to each of these warehouses are $\$ 18, \$ 16$, and $\$ 14$ per system, respectively. What shipping schedule will enable Acrosonic to meet the warehouses' requirements and at the same time keep its shipping costs to a minimum?

Solution

VerifiedUse the sketch below to define the nonnegative variables representing the number of units shipped from (Plant I or II) to (Warehouse A,B, or C)

The object is to minimize the cost of shipping, which is, according to the text,

$\boldsymbol{C=16x_{1}+20x_{2}+22x_{3}+18x_{4}+16x_{5}+14x_{6}}\rightarrow\min$

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