Hawkins Manufacturing Company produces connecting rods for 4- and 6-cylinder aut

Question

Hawkins Manufacturing Company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $1,700, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,900. Manufacturing costs are $14 for each 4-cylinder connecting rod and $19 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If a production changeover is necessary from one week to the next, the weekend is used to reconfigure the production line. Once the line has been set up, the weekly production capacities are 6,900 6-cylinder connecting rods and 7,600 4-cylinder connecting rods.

Let
x4 = the number of 4-cylinder connecting rods produced next week
x6 = the number of 6-cylinder connecting rods produced next week
s4= 1 if the production line is set up to produce the 4-cylinder connecting rods; 0 if otherwise
s6 = 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise

Using the decision variables x4 and s4, write a constraint that limits next week's production of the 4-cylinder connecting rods to either 0 or 7,600 units.

x4   s4

Using the decision variables x6 and s6, write a constraint that limits next week's production of the 6-cylinder connecting rods to either 0 or 6,900 units.

x6   s6

Write three constraints that, taken together, limit the production of connecting rods for next week.

x4   s4

x6   s6

s4 +  s6   

Write an objective function for minimizing the cost of production for next week.

Min  x4 +  x6 +  s4 +  s6

Explanation / Answer

Using the decision variables x4 and s4, write a constraint that limits next week's production of the 4-cylinder connecting rods to either 0 or 7,600 units.

x4*s4 7600

Using the decision variables x6 and s6, write a constraint that limits next week's production of the 6-cylinder connecting rods to either 0 or 6,900 units.

x6*s6 6900

Write three constraints that, taken together, limit the production of connecting rods for next week.

x4*s4 7600

x6*s6 6900

s4 + s6 = 1

Write an objective function for minimizing the cost of production for next week.

Min 14x4 + 19x6 + 1700s4 + 3900s6

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