3. Product Pricing. Phillips Inc. produces two distinct products, A and B. The products do not compete with each other in the marketplace; that is, neither cost, price, nor demand for one product will impact the demand for the other. Phillips\" analvsts have collected data on the effects of advertising on profits. These data suggest that, although higher advertising correlates with higher profits, the marginal increase in prots diminishes at higher advertising levels, particularlv for product 0. Analvsts have estimated the following functions: Annual prot for producta = 1.2?12LN(X,.) + 1141-1 Annual profit for productB = 0.30?0LN[J{'3] + 16.100 where I}, and XE are the advertising amount allocated to products A and B, respectivelv, in thousands of dollars, profit is in millions of dollars, and LN is the natural logarithm function. The advertising budget is $500,000, and management has dictated that at least $50,000 must be allocated to each of the two products. Build an optimization model that will prescribe how Phillips should allocate its marketing budget to maximize profit. 4. Estimating Economic Output. The Cobb-Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the form f (L, C) = COLGCC2 where co, c1, and c2 are constants. The variable L represents the units of input of labor, and the variable C represents the units of input of capital. In this example, assume co = 5, c1 = 0.25, and c2 = 0.75. Assume each unit of labor costs $25 and each unit of capital costs $75. With $75,000 available in the budget, develop an optimization model to determine how the budgeted amount should be allocated between capital and labor in order to maximize output