Backyard Helpers, Inc. is a small manufacturing company with $18$ different gardening tools in its product line. All of the products are fabricated using the same equipment.

Recently, sales demand has increased. Unfortunately, Backyard Helpers cannot produce enough products with existing equipment to meet that demand. Facilities can be expanded, and new equipment purchased, but it will be at least two years before that happens. The production manager needs to make production scheduling decisions now.

The data to the right includes assumed information about demand, sales price, cost, and fabrication time on the shared equipment for each of Backyard Helpers' products.

Maximum machine time is $40,500$ minutes per month. The demand for all products is spread equally throughout the month. Fixed costs $($manufacturing$,$ selling, and administrative$)$ total $$755,750$ per month. Backyard Helpers maintains no inventory of finished goods: all units produced are sold during the month.

Required

a$.$ Ignore machine time limits in answering the following:

Which product has the highest contribution margin per unit? How many units of that product should be produced each month?

If Backyard could meet demand, what would be the total net operating income per month?

b$.$ If demand was unlimited for all products, which products should Backyard Helpers produce?

c$.$ Given the maximum number of machine minutes per month and the expected demand per month, use Solver in Excel to answer the four questions that follow. To prepare your worksheet to use the Solver tool, add columns with formulas for $(1)$ contribution margin per unit, $(2)$ total quantity in units, $(3)$ total machine minutes, and $(4)$ total contribution margin. In the Solver tool window, enter the cell that you would like to maximize $($Hint: It is a single cell$),$ Identify the variables $($Hint: Use quantity in units column$)$ and enter the constraints $($Hint: There are two constraints relating to demand and machine minutes$).$

How many of the following products should be produced each month?

i$.R25$

ii$.$ JK$369$

Which products would be temporarily eliminated from Backyard Helpers product line under the Excel solution?

What is the total net operating income per month given the machine time constraints and the quantities determined

by Solver?

What is the maximum amount Backyard Helpers should be willing to pay to rent fabrication time from another company? $($Assume transportation and other costs would total $$50,000.)$

d$.$ In Questions c$\mathrm{.}2,$ you identified products that would be temporarily eliminated if Backyard followed the Excel solution. What reasons, if any, might management have for continuing to produce some of those products even if it means reducing the supply of some of the other products?