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Exercise 4. One company produces tools in two workshops and sells them to three customers. The cost of producing 1000 tools in a workshop and shipping them to a customer is shown in the tablebelow: Customer 1 Customer 2 Customer 3 Workshop 1 $60 $30 $160 Workshop 2 $130 $70 $170 Customers 1 and 3 pay $200 per thousand tools; Customer 2 pays $150 per thousand tools. To produce 1000 tools in Workshop 1, it takes 200 hours of work and 300 hours in workshop 2. A total of 5,500 hours of labour is available in both workshops. Additional hours of work can be purchased at $20 per hour of work. Plant 1 can produce up to 10,000 tools and Plant 2 can produce up to 12,000 tools. Each customer's request is supposed to be unlimited. Subject to C11 X11 - 1 X12 - 1X13 - 10 C21 X21 - 1 X22 - 1X23 - 12 C3200 X11 - 200 X12 - 200 X13 - 300 X21 - 300 X22 - 300 X23-1 L-5500 B H J K L M c X12 D X13 E X21 F 022 G X23 X11 L A 1 2 3 Solution 10.00 0.00 0.00 0.00 11.67 000 0.00 5 Profit $140 $120 $40 $70 $80 $30 Total $2,333 33 $20 SEN- 8 C1 9 C2 10 0 1 0 200 1 0 200 1 0 200 o- 0 1 RHS 10.00 10 11.67 - 12 F6000 560 1 30 0 0 - 1 1 200 6 Adjustable Cols 8 Cell Name 9 SDS3 Solution X11 10 $C$3 Solution X12 11 $D$3 Solution X13 12 SESS Solution 21 13 $F$3 Solution X22 14 $653 Solution X23 15 SH53 Solution L 16 17 Constraints Final Value 10 0 0 0 1167 U 0 Reduced Objective Cost Coefficient 140 120 -100 40 -10 70 0 80 -50 30 -1972 -20 Allowable Increase 1E+20 20 100 10 130 50 19.73 Allowable Decrease 20 1E430 1E+30 1E+30 10 15.30 1E+30 Final Value 10 SEBE Cell Name $1$8 CI RHS 5159 C2 RHS $I$10 C3 RHS Shadow Constraint Price R.H. Side 86 67 10 000 12 D 27 9800 Allowable Increase 175 1E+30 100 Allowable Decrease 0.50 03 3500.00 5800 (The following three questions are independent of each other.) Question 4.1 (5 pts.) If it cost $70 to produce 1,000 tools at Shop 1 and ship them to Customer 1, what would be the new solution to the problem and benefit? Question 4.2 (5 pts.) If the price of an additional hour of work were reduced to $4, would the company buy additional labour? Justify your answer. Question 4.3 (10 pts.) A consultant proposes to increase the production capacity of Plant 1 by 100 tools at a cost of $5. Does the company have to accept the offer? (Final value: final value, reduced cost: reduced cost, allowable increase: allowable increase, allowable decrease: allowable red low price: shadow cost, ombre, constraint R.H. side: constraint on the right) D (Ctrl)