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A 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 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.

	Ohio Region		California Region
	March	April	March	April
Dry	1200	4500	1500	3300
Wet	2500	4200	1200	3800

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.

	Ohio Region		California Region
	March	April	March	April
Regular	23	20	22	19
Overtime	4	5	5	6

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

	Ohio Region		California Region
	Regular	Overtime	Regular	Overtime
Dry	200	250	180	240
Wet	180	230	210	250

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 the Ohio plant, the cost of holding inventory is $1.5 per unit for dry food and $2 per unit of wet food

In the California plant, the cost of holding inv $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.

	Ohio Region		California Region
	Regular	Overtime	Regular	Overtime
Dry	30	40	35	45
Wet	33	45	32	42

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

- How much each plant should sell each product in each month

- How much each plant should sell each product in each month to the other plants 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).

DO NOT SOLVE THE PROBLEM USING EXCEL SOLVER.

Answer the following:

Assumptions or additional data used

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

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