Question

VENTURE CAPITAL. Delta Venture Capital Group is considering whether to invest in Maytime Products, a new company that is planning to compete in the small kitchen appliance market. Maytime has three products in the design and test phase: (1) a unique refrigerator/oven that can be programmed in the morning to cook foods (like chicken) but keeps the food refrigerated until the cooking process begins; (2) a French fry maker that can make long thick French fries or small thin shoestring fries; and (3) a French toast maker that cooks French toast of any size evenly on the top and bottom simultaneously.

Delta’s primary concern is how much money it must invest with Maytime 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. Delta would have to commit to the $2,000,000 and then would like to minimize its total variable cost outlay until Maytime turns a profit (i.e., until Maytime can cover the initial $2,000,000 investment with profits (selling price variable cost) from its sales.)

Product	Selling Price	Variable Cost	Initial Demand
Refrigerator/Oven	$240	$140	5000
French Fry Marker	$85	$50	4000
French Toast Marker	$63	$36	2300

Maytime will initially produce no more than 15,000 units of any of the items but will meet anticipated initial demand. What production quantities for the products will minimize the total variable cost of the items produced while attaining a “profit” of $2,000,000?

Answer 1

The optimal production quantity of each product is determined by linear optimization model as under

Formula:

F2 =E2*B2 copy to F2:F4

G2 =E2*C2 copy to G2:G4

H2 =F2-G2 copy to H2:H4

F5 =SUM(F2:F4) copy to F5:H5

Optimal production quantities are as under:

Product	Production quantity
Refrigerator / Oven	15,000
French Fry Marker	12,511
French Toast Marker	2,300