Question

the management of the albert hanson company is trying to determine the best product mix for two new products. because these products would share the same production facilities, the total number of units produced of teh two prodcuts combined cannot exceed two per hour. because of uncertainty about how well these products will sell, the profit from producing each product provides decreasing marginal returns as the production rate is increase. in particular, with a p production rate of R1 units per hour, it is estimated that product 1 would provide a profit per hour of $200R1-$100R1^2. if the production rate of product 2 is R2 units per hour, its estimated profit per hour would be $300R2-$100R2^2. formulate a quadratic programming model in algebraic form for determining the product mix that maximizes the total profit per hour. formulate and solve this model on a spreadsheet. SHOW ALL WORK

Answer 1

Production rate for product 1 = R1

Production rate for product 2 = R2

Profit for R1 production rate is 200R1 - 100R1^2

Profit for R2 prodcution rate is 300R2 - 100R2^2

R1 + R2 <= 2 is the constraint of production per hpur