Reference no: EM133174598

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 $2300, and the cost required to set up the production line for the 6-cylinder connecting rods is $3600. Manufacturing costs are $13 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 there is a production changeover 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 5600 6-cylinder connecting rods and 7600 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

1. 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 7600 units. Fill in the blank 1x₄fill in the blank 3s₄
2. 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 5600 units.
3. Write three constraints that, taken together, limit the production of connecting rods for next week. 
4. Write an objective function for minimizing the cost of production for next week.