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Example. A product mix problem

The Monet Company produces four types of picture frames, which we label 1,2,3,4. The four types of frames differ with respect to size, shape, and materials used. Each type requires certain amount of skilled labor, metal and glass (as shown in Table 2). This table also lists the unit selling price Monet charges for each type of frame. During the coming week, Monet can purchase up to 4000 hours of skilled labor, 6000 ounces of metal, and 10000 ounces of glass. The unit costs are $8.00 per labor hour, $0.50 per ounce of metal, and $0.75 per ounce of glass. Also market constraints are such that it is impossible to sell more that 1000 type 1 frames, 2000 type 2 frames, 500 type 3 frames and 1000 type 4 frames, and Monet does not want to keep any frames in inventory at the end of the week end. What should the company do to maximize its profit for this week?

Table. Resources allocation Frame 1 Frame 2 Frame 3 Frame 4 Skilled labor 2 1 13 2 Metal Glass 6 2 11 Selling price $28.50 $12.50 $29.25 $21.50