Chapter 11 - Wisniewski

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-4x = -40

x = 10

Substitute the value for x into one of the constraints and solve for y

Nutrient A 2(10)+ 2y = 80

20+ 2y = 80

2y = 60

y = 30

The intersection of the Nutrient A and Nutrient C constraints forms another corner of the feasible region so the coordinates must be calculated.

There are multiple ways to approach finding the coordinates. I multiplied both sides of the Nutrient A equation by -6 and added the equations together

Nutrient A -6(2x + 2y) = -6(80)

-12x + -12y = -480

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Nutrient B -12x + -12y = -480

Nutrient C 4x + 12y = 240

-8x = -240

x = 30

Substitute the value for x into one of the constraints and solve for y

Nutrient A 2(30)+ 2y = 80

60+ 2y = 80

2y = 20

y = 10[pic 6]

Determine which corner point minimizes weekly cost

(60,0) 8(60) + 10(0) = $480/week [pic 7]

(30,10) 8(30) + 10(10) = $340/week

(10,30) 8(10) + 10(30) = $380/week

(0,60) 8(0) + 10(60) = $600/week

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Toy Manufacturing Problem

- The company is considering raising the price of Trucks in order to increase profit per unit (you can assume that costs do not change). How much can the price be increased without changing the optimal solution?

From the Sensitivity Report for the Toy Problem we can see that the price of the Toy Trucks can be raised by up to $3 (resulting in an increase in profit of $3/truck) without changing the optimal solution.

- The company is considering increasing machine capacity in order to increase profit. Which machines should the company consider? How much additional capacity should be added and how much would profit increase?

Each additional hour of capacity added on Machine B would increase profit by $1.50 up to an additional 20 hours.

Alternatively, each additional hour of capacity in Finishing would increase profit by $0.50 up to an additional 13.3 hours.

If you had to choose which machine to add capacity to, you can see that adding capacity to Machine B would increase profit by up to $30 ($1.5/hour * 20 hours). You can also see that adding capacity to Finishing would increase profit by up to $6.67. Therefore, it would be preferable to add capacity to Machine B because the potential profit increase is greater.

Fertilizer Problem

- How much can the price of Blend II increase without changing the optimal solution?

From the Sensitivity Report for the Fertilizer Problem we can see that the price of the Blend II can be decrease by up to $2/bag without changing the optimal solution.

- Scientific research shows that increasing the amount of Nutrient C will improve production. How much will it cost the producer to increase the amount of Nutrient C, and what is the maximum allowable increase?

The producer can increase the amount of Nutrient C added per week by up to 160 units. The cost will increase by $0.25 for each additional unit added.

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