Solve the problem.A furniture manufacturer makes TV tables and bookcases in the same workshop. Each item brings in a profit of $18. Each bookcase requires 2 hours of labor 3 units of teak wood. Each TV table requires 6 hours of labor and 1 unit of teak wood. Resources in the workshop are restricted to 6 units of teak wood a day and 12 hours of labor per day. The initial and final tableaux are given below with x = the number of TV tables and y = the number of bookcases produced each day.??

style="vertical-align: -49.0px;" />(initial)(final)(a)What is the optimal production schedule and maximum daily profit?(b) If the amount of available teak wood can be increased to 10 units per day, how does the production schedule change? How do maximum profits change?(c) If the amount of teak changes by h units in a day, how would the optimal production schedule and maximum profit change?(d) What restrictions should be placed on the size of h to make the analysis in (c) valid?

What will be an ideal response?

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(a)	x = , y = , M = $54

(b) x = 1, y = 3: Make 1 TV table and 3 bookcases per day; M = $72
 

(c)	x =  -  h, y =  +  h, and M = 54 +  h.

(d) -4 ? h ? 12

Mathematics