Mack Co. manufactures four different products. Because the quality of its products is high, the demand for them is more than the company can produce. Based on the enquiries made by the current and potential customers, you have estimated the following for the coming year:

Product A: Estimated demand in units = 8,000 Sell price per unit = $50 direct materials cost per unit = $5 and direct labour cost per unit = $5

Product B: Estimated demand in units = 24,000 Sell price per unit = $60 direct materials cost per unit = $10 and direct labour cost per unit = $9

Product C: Estimated demand in units = 20,000 Sell price per unit = $150 direct materials cost per unit = $25 and direct labour cost per unit = $30

Product D: Estimated demand in units = 30,000 Sell price per unit = $100 direct materials cost per unit = $15 and direct labour cost per unit = $20

The following info is also available:

1. the direct labour rate is $15 per hour and the factory has a capacity of 80,000 hours. For the next year, Mack is unable to expand this capacity.
2. Mack is unwilling to increase its selling prices
3. Apart from direct materials and direct labour, the only other variable expense is variable overhead. the variable overhead is 50% of the direct labour cost
4. fixed manufacturing overhead is estimated to be $1 million for the coming year. Fixed marketing and admin expenses are estimated to be $750,000 for the coming year

PROBLEM: calculate the contribution margin and prepare incremental analysis for maximizing operating income. Determine which products and how many units of each Mack should produce in the coming year to maximize its operating income

My Textbook provides one answer = produce 11,467.50 units of C. Please show me how to solve this.

*** please do NOT answer this using excel.