4. The Volta Battery Company manufactures AA, A. C, and D batteries in each of four plants. The daily production (in 1000's) for the four plants is given the following table:
(a) The vectors that represent the production at the various plants are not linearly independent. Show this and find a dependency equation.
(b) The company has contracted to provide 56000 AA, 53000 A. 59000 C, and 40000 D batteries to an electronics distributor. This demand is currently met by operating plant I for 3 days, plant 2 for 3 days, plant 3 for 4 days and plant 4 for 3 days. Determine if it is possible to close one of the plants and meet the production demands with only three plants. If it is possible. what are the feasible production schedules? Assume that each plant can be operated up to 7 days per week.
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(a) We want to find a, b, c such that:
In matrix form, M =
We want to reduce M to RREF form, if possible. We proceed as follows:
= (R2R2 - R1, R3R3 - R1)
= (R1R1 ...
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