Calvin Klein has lotions that come in three sizes. 4,8,12 ounces. The following table summarizes the selling prices and variable costs per case of each lotion size.
Per case:
4 ounce : Price $ 36 , variable cost $13
8 ounce : Price $66, variable cost $24.50
12 ounce: Price $72, variable cost $27
Fixed costs are $771,000 , current production and sales are 2,000 cases of 4 ounce bottles, 4000 cases of 8 ounces bottles, and 1000 cases of 12 ounces bottles. Calvin Klein typically sells the three lotion sizes in fixed proportions as represended by the preceding sales amounts.
How many cases of 4,8,12 ounce lotion bottles must be produced and sold for calvin klein to break even, assuming that the three sizes are sold in fixed proportions?