Question

Gale wants to determine the values of X1 and X2 to maximize total profit. The linear model and the sensitivity report are given as below. Round to two decimal places. [Note: X1 = number of Product 1, X2 = number of Product 2]. Max Z 30X1 + 40X2 = C1: 2X1 + X2 ≤ 40 C2: X1 + 2X2 < 10 C3: 2X1 + X2 ≤ 50 C4: 3X1 + 3X2 ≤ 85 C5: Xi ≥ 0 Variable Cells Cell $B$3 $C$3 Constraints Name X1 X2 Name Cell $M$6 C1 $M$7 C2 $M$8 C3 $M$9 C4 Material 1 (tons) Material 2 Material 3 Material 4. Final Value 10 Final Value 0 20 10 20 30 Reduced Objective Allowable Allowable Coefficient Increase Cost Decrease 1E+30 20 0 -20 30 40 Shadow Constraint Allowable Price R.H. Side Increase 0 30 0 0 40 10 50 85 1E+30 10 1E+30 1E+30 10 1E+30 Allowable Decrease 20 10 30 55 Your Webcar A local supplier offers to sell Gale 9 tons of Material 2 for $25.00 per ton. What should he do? O refuse to buy any Material 2 O buy 9 tons of Material 2 for $25.00 per ton Question 16 By how much would total profit increase if he could increase the number of tons of Material 2 from 10 to 15 tons? 00 05 8 pts O 10

Answer 1

Cost of raw materials is debited to Raw Materials Inventory when the materials are put into production. bill for the materials is paid. materials are ordered .

By how much would total profit increase if he could increase the number of tons of Material 2 from 10 to 15 tons?The linear model and the sensitivity report given below:Max Z 30X1 + 40X2 = C1: 2X1 + X2 ≤ 40 C2: X1 + 2X2 < 10 C3: 2X1 + X2 ≤ 50 C4: 3X1 + 3X2 ≤ 85 C5: Xi ≥ 0 .

Given that X1 is the number of Product 1 and X2 is the number of Product 2.Total Profit = 30X1 + 40X2To maximize total profit, the value of X1 and X2 should be determined. Given that Gale is offered to purchase 9 tons of Material 2 for $25.00 per ton.

Now, let's determine the total profit by keeping the value of X2 at 10 and then at 15.X2 = 10Maximum value of X1 can be calculated by keeping the value of X2 at 10.2X1 + X2 ≤ 40When X2 = 10, 2X1 ≤ 30So, X1 ≤ 15Maximum value of Z = 30X1 + 40X2= 30(15) + 40(10)=$1050X2 = 15

Maximum value of X1 can be calculated by keeping the value of X2 at 15.2X1 + X2 ≤ 40When X2 = 15, 2X1 ≤ 10So, X1 ≤ 5Maximum value of Z = 30X1 + 40X2= 30(5) + 40(15)=$750 + $600= $1350When the number of tons of Material 2 is increased from 10 to 15 tons, the total profit increases by $300. Answer: 300.