Byers Venture Capital Group is considering whether to invest in Wheeler Products, a new company that...

 

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Byers Venture Capital Group is considering whether to invest in Wheeler Products, a new company that is planning to compete in the small kitchen appliance market. Wheeler has three products in the design and test phase: a unique refrigerator/oven that can be programmed in the morning to cook food (like chicken) but keeps the food refrigerated until the cooking process begins; a French fry maker that can make long thick French fries or small thin shoestring fries; a French toast maker that cooks French toast of any size evenly on the top and bottom simul- taneously. Byers's primary concern is how much money it must invest with Wheeler before it will show a profit. The company will need an immediate initial investment of $2,000,000 to secure a plant and cover overhead costs. This investment must be paid back with initial profits. The following table gives the anticipated selling price, the variable cost per unit manufactured, and the initial demand for each product obtained through market research. Byers would have to commit to the $2,000,000 and then would like to minimise its total variable cost outlay until Wheeler turns a profit (i.e., until Wheeler can cover the initial $2,000, 000 investment with profits (=selling price - variable cost) from its sales.) Product Refrigerator/Oven French Fry Maker French Toast Maker Selling price ($) Variable cost ($) Initial demand 240 85 63 140 50 36 Table 2: Wheeler Products data 5000 4000 2300 Wheeler will initially produce no more than 15,000 units of any of the items but will meet anticipated initial demand. Formulate an LP and determine what production quantities for the products will minimise the total variable cost of the items produced while attaining a "profit" of $2,000,000. Byers Venture Capital Group is considering whether to invest in Wheeler Products, a new company that is planning to compete in the small kitchen appliance market. Wheeler has three products in the design and test phase: a unique refrigerator/oven that can be programmed in the morning to cook food (like chicken) but keeps the food refrigerated until the cooking process begins; a French fry maker that can make long thick French fries or small thin shoestring fries; a French toast maker that cooks French toast of any size evenly on the top and bottom simul- taneously. Byers's primary concern is how much money it must invest with Wheeler before it will show a profit. The company will need an immediate initial investment of $2,000,000 to secure a plant and cover overhead costs. This investment must be paid back with initial profits. The following table gives the anticipated selling price, the variable cost per unit manufactured, and the initial demand for each product obtained through market research. Byers would have to commit to the $2,000,000 and then would like to minimise its total variable cost outlay until Wheeler turns a profit (i.e., until Wheeler can cover the initial $2,000, 000 investment with profits (=selling price - variable cost) from its sales.) Product Refrigerator/Oven French Fry Maker French Toast Maker Selling price ($) Variable cost ($) Initial demand 240 85 63 140 50 36 Table 2: Wheeler Products data 5000 4000 2300 Wheeler will initially produce no more than 15,000 units of any of the items but will meet anticipated initial demand. Formulate an LP and determine what production quantities for the products will minimise the total variable cost of the items produced while attaining a "profit" of $2,000,000.

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