The Kira Company has two plants (in Ohio and California) on opposite sides of the United States. Each of these plants produces the same two products (Dry and Wet kitten food) and then sells them to wholesalers within its half of the country. The orders from wholesalers have already been received for the next two months (March and April), where the numbers of units requested are shown in Table 1. The company is not obligated to completely fill these orders but will do so if it can without decreasing its profits.)

Table 1: Monthly demand for dry and wet kitten food in Ohio and California regions.

The available production days in March and April for Ohio and California plants are given in Table 2, whereas the production rates for each product (number of units produced per day devoted to that product) in each plant is displayed in Table 3.

Table 2: Available regular time and overtime production days in Ohio and California plants.

Table 3: Daily production capacities with regular time and overtime in Ohio and California plants.

Inventories are depleted at the end of February, but each plant has enough capacity to hold 1200 units total of the two products if an excess amount is produced in March for sale in April. In Ohio plant, the cost of holding inventory is $1.5 per unit for dry food and $2 per unit of wet food, whereas inventory holding cost in California plant is $2 per unit for dry food and $2.5 per unit of wet food.

The production cost per unit produced of each product is shown in Table 4 below for each plant.

Table 4: Unit production cost for dry and wed kitten food in Ohio and California regions.

The net sales revenue (selling price minus normal shipping costs) the company receives when a plant sells the products to its own customers (the wholesalers in its half of the country) is $50 per unit of Dry food and $52 per unit of Wet food. However, it is also possible (and occasionally desirable) for a plant to make a shipment to the other half of the country to help fill the sales of the other plant. When this happens, an extra shipping cost of $12 per unit per Dry food and $8 per unit of Wet food is incurred.

Management now needs to determine how much of each product should be produced in each plant during each month, as well as how much each plant should sell each product in each month and how much each plant should sell each product in each month to the other plant's customers. The objective is to determine which feasible plan would maximize the total profit (total net sales revenue minus sum of production costs, inventory costs, and extra shipping costs).

Answer the following:

Assumptions or additional data used

Mathematical formulation
- Define decision variables.
- Formulate objective function and constraints.

Computer solution: Solve the problem using excel solver.

Sensitivity Analysis: In particular, answer the following questions:
- If you are able to increase the capacity of one of the warehouses, which one would you select? How much will you be willing to pay per unit capacity increase?

- You must schedule one half-day training program in each plant either in March or April during the regular production days. Plants will not produce during the training sessions. Which month would you prefer to schedule the training in Ohio and California plants?