The Ace Manufacturing Company has orders for three similar products:

ProductOrder (Units)A2050B500C1150

Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are as follows:

MachineCapacity (Units)115002160031000

ProductMachineABC1$0.80$1.30$0.802$1.30$1.30$1.503$1.10$0.90$1.50

Use the transportation model to develop the minimum cost production schedule for the products and machines. Show the linear programming formulation. If required, round your answers to one decimal place.

The linear programming formulation and optimal solution are shown.

Letx1A Units of product A on machine 1 x1B=Units of product B on machine 1 x3C=Units of product C on machine 3

Minfill in the blank 1x_1A+fill in the blank 2x_1B+fill in the blank 3x_1C+fill in the blank 4x_2A+fill in the blank 5x_2B+fill in the blank 6x_2C+fill in the blank 7x_3A+fill in the blank 8x_3B+fill in the blank 9x_3C s.t. fill in the blank 10x_1A+fill in the blank 11x_1B+fill in the blank 12x_1C fill in the blank 13 fill in the blank 14x_2A+fill in the blank 15x_2B+fill in the blank 16x_2C fill in the blank 17 fill in the blank 18x_3A+fill in the blank 19x_3B+fill in the blank 20x_3Cfill in the blank 21 fill in the blank 22x_1A +fill in the blank 23x_2A+ +fill in the blank 24x_3A =fill in the blank 25 fill in the blank 26x_1B +fill in the blank 27x_2B +fill in the blank 28x_3B =fill in the blank 29 fill in the blank 30x_1C +fill in the blank 31x_2C +fill in the blank 32x_3C=fill in the blank 33x_ij 0 for all i, j

Optimal SolutionUnitsCost1-Afill in the blank 34$fill in the blank 351-Bfill in the blank 36$fill in the blank 371-Cfill in the blank 38fill in the blank 392-Afill in the blank 40fill in the blank 412-Bfill in the blank 42$fill in the blank 432-Cfill in the blank 44$fill in the blank 453-Afill in the blank 46fill in the blank 473-Bfill in the blank 48fill in the blank 493-Cfill in the blank 50$fill in the blank 51 Total $fill in the blank 52