algebra A firm has two plants that produce outputs of three different goods. Its total labour force is fixed. When a fraction $\lambda$ of its labour force is allocated to its first plant and a fraction $1-\lambda$ to its second plant (with $0 \leq \lambda \leq 1$ ), the total output of the three different goods are given by the vector $\lambda(8,4,4)+(1-\lambda)(2,6,10)=(6 \lambda+2,-2 \lambda+6,-6 \lambda+10)$.
(a) Is it possible for the firm to produce either of the two output vectors $a$ $=(5,5,7)$ $b$ = $(7,5,5)$ if output cannot be thrown away?
(b) How do your answers to part (a) change if output can be thrown away?
(c) How will the revenue-maximizing choice of the fraction $\lambda$ depend upon the selling prices $\left(p_1, p_2, p_3\right)$ of the three goods? What condition must be satisfied by these prices if both plants are to remain in use? 8th Edition•ISBN: 9781305585126 (6 more)N. Gregory Mankiw 15th Edition•ISBN: 9780073401805 (8 more)Douglas A. Lind, Samuel A. Wathen, William G. Marchal 12th Edition•ISBN: 9780134163451 (3 more)Barry Render, Chuck Munson, Jay Heizer 10th Edition•ISBN: 9781337902571 (1 more)Eugene F. Brigham, Joel Houston