A Company Manufactures Four Grades of Videotape: Normal, Extra, Super $\vec { a } = \left( a _ { 1 } , a _ { 2 } , a _ { 3 } , a _ { 4 } \right)$

Essay

A company manufactures four grades of videotape: Normal, Extra, Super, and Supreme.Last year, the company sold a₁ boxes of Normal tapes for $5.00 each, a₂ boxes of Extra tapes for $5.50 each, a₃ boxes of Super for $6.00 each, and a₄ boxes of Supreme for $8.00 each.Let $\vec { a } = \left( a _ { 1 } , a _ { 2 } , a _ { 3 } , a _ { 4 } \right)$ , $\vec { b } = ( 5,5.5,6,8 )$ , and $\vec { C } = ( 2,2.4,2.5,3 )$ .
(a)Compute $\vec { a } \cdot \vec { b } - \vec { a } \cdot \vec { C }$ .
(b)If the computation in part (a)represents the company's profit last year, then what does the vector $\vec { C }$ represent?