Problem $3.$ The senior management at ABC would like to determine if it is possible to improve firm profitability by changing their existing product mix. Currently the product mix is determined by giving resource priority to the highest contribution margin. The company has $10$ workers on hand, each worker is paid $$25$ per hour. Overhead costs are $$35,000$ per week. The plant operates $18$ hours per day and $6$ days per week. Labor is considered a fixed expense because workers are paid for their time regardless of their utilization. Detailed production information is provided below.

Model A

Model B

Model C

Price

$$400$

$$360$

$$390$

Material Cost

$$50$

$$40$

$$110$

Weekly demand

$100$

$75$

$40$

Processing time Station $1$

$60$ min

$0$ min

$30$ min

Processing time Station $2$

$0$ min

$0$ min

$60$ min

Processing time Station $3$

$10$ min

$60$ min

$0$ min

Processing time Station $4$

$20$ min

$30$ min

$40$ min

What is the product mix that yields the maximum total gross profit? What is the resulting profit?