Connolly Company produces two types of lamps, classic and fancy, with unit contribution margins of $13 and $21, respectively. Each lamp must spend time on a special machine. The firm owns four machines that together provide 18,000 hours of machine time per year. The classic lamp requires 0.20 hours of machine time, the fancy lamp requires 0.50 hours of machine time. A maximum of 60,000 units of each lamps can be sold. What is the total contribution margin of the optimal mix of classic and fancy lamps?

Total contribution margin of the optimal mix =$ 1,032,000

Explanation:

Whenever a company is faced with a limiting factor i.e a resource in short supply, the company should allocate the resource to the product with he highest contribution per unit of the scare resource

Product       Cont/unit       machine hr /unit      cont/hr           Ranking

classic            $13 per unit  0.2 hour                  65 per hour       Ist

Fancy              $21 per unit  0.5 hour                 $42  per hour    2nd

The company should use all of its limited 18,000 machine hours  to produce the two products as follows:

Product   units     machine hr /unit   Machine hours    Total contribution

Classic   60,000        0.2                         12,000             780,000

Fancy      12,000**          0.5                       6,000 *           252,000

                                                               18,000                $ 1,032,000

Total contribution margin of the optimal mix =$ 1,032,000

* this represent balance of machine hours after 12,000 had been devoted to the production of classic

** This is quantity of Fancy that can be produced using 6000 hours

= 6000/0.5 = 12,000 units