Question

Cardinal Manufacturing is seeking to optimize its profitability related to production of two main goods: hammers and shovels. In order to produce a lot of 100 hammers Cardinal needs 50 pounds of steel and 35 pounds of wood. The profit per lot of hammers is $170. In order to produce a lot of 100 shovels, Cardinal needs 75 pounds of steel and 80 pounds of wood. The profit per lot shovels is $260. The factory material throughput is limited to 1400 pounds of steel and 1600 pounds of wood per day.   One additional constraint is that the factory must produce at least 2 lots of each product per day. What is the optimal number of production lots of each product and the resulting profit? Show your work in developing the optimized answer.

Answer 1

Formulate LP model s follows:

Let X be the number of production lots of hammers to be produced

and Y be the number of production lots of shovels to be produced

Maximize Z = 170X+260Y

s.t.

50X+75Y <= 1400

35X+80Y <= 1600

X, Y >= 2

Solution is determined using LINGO as follows:

Optimal solution:

Production lots of hammers to be produced, X = 2

Production lots of shovels to be produced, Y = 17.33

Total profit = $ 4846.67

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In the above solution, integer constraints are not applied to variables. Considering integer constraints, the LINGO model and solution is as follows:

Solution:

Production lots of hammers to be produced, X = 4

Production lots of shovels to be produced, Y = 16

Total profit = $ 4840